The Toffees had the best chance of a goalless opening 45 minutes as Phil Jagielka prodded the ball wide from close range, following Michael Keane's headed knockdown.
Walcott struck five minutes after the restart, keeping his composure in a congested penalty box to power a shot into the top corner for his first goal in nine matches.
Newcastle struggled to create clear-cut equalising chances although they could have had an 87th-minute penalty when the ball arguably struck Jagielka on the arm.
Relive how the action unfolded on Merseyside with Sports Mole's minute-by-minute updates below.
7.00pmThe Premier League weekend concludes at Goodison Park as Everton host Newcastle United, with the two sides jostling for position in the middle of the table. A win tonight would lift the Magpies above their hosts and be a fifth in a row for the in-form team in the division. Team news coming up...
7.06pmThe Toffees are unchanged from the 1-1 draw with Swansea City last time out, with Wayne Rooney again deployed in the midfield three. Gylfi Sigurdsson and Mason Holgate are still missing with knee and ankle injuries respectively.
7.08pmRooney has been susbtituted in each of Everton's last four matches, twice before the hour mark which has seemingly caused some tension between him and Allardyce, but the ex-England captain retains his starting place over Tom Davies.
7.10pmAfter an unwanted transformation to heroic Swansea leader to hapless Everton liability, Ashley Williams is again left out of the squad. The Welshman has not featured since being sent off against Burnley in the first week of March, with Ramiro Funes Mori fit again to provide defensive cover on the bench.
7.12pmThe goals have dried up a little for January signings Cenk Tosun and Theo Walcott. The Turkish striker looked like he was adapting to English football with four goals in three matches, but has now gone three without a goal, while Walcott is goalless in nine after a brace on his second appearance.
7.14pmHaving named an unchanged lineup for the last four matches, all of which have been victories, Rafael Benitez dares to change a winning formula by handing Islam Slimani a full debut in place of Dwight Gayle. The on-loan Leicester City striker has been great as an impact sub in the last two matches.
7.16pmMohamed Diame put in a man-of-the-match performance against the Gunners last weekend and has been an unlikely hero of Newcastle's post-Christmas rise up the table, having struck up a perfectly-balanced partnership of power and finesse with Jonjo Shelvey, who has been in equally good form.
7.18pmWith the fresh impetus of Kenedy and Shelvey and Matt Ritchie providing a quality supply line, Newcastle have been much more of a scoring threat in recent weeks and Ayoze Perez has been the beneficiary, scoring in each of his last three games to more than double his league tally for the season.
7.20pmShould Perez score in four consecutive Premier League games for Newcastle, he would be the first player to do so since Papiss Cisse netted in six in a row from March to April 2012. Remember that, when Papiss Cisse was the best striker in the world for a couple of weeks?
7.22pmIt was Alan Pardew who brought Cisse to Newcastle, and he was the last United boss to win five Premier League games in a row back in November 2014 which is a sequence that Benitez's boys will be looking to match on Merseyside this evening.
7.24pmThe Magpies have actually only lost one of their last nine matches, although that was on Merseyside when they suffered a 2-0 defeat to Liverpool last month. They look a completely different side to the one which twice surrendered before kickoff against Manchester City either side of the New Year.
7.26pmSpeaking of New Year, it was a 1-0 win at Stoke City on January 1 of this year which ended a horrible run of Monday-night travel sickness for Newcastle, who had lost 10 away games in a row on a Monday prior to their victory at the Britannia Stadium.
7.28pmThe win over the Potters is a part of a much-improved run of results on the road for the Magpies, who have collected 11 points from their last seven away matches, which is more than they had managed in their previous 22 away top-flight outings.
7.30pmThis turnaround has helped Benitez's side climb from one point above the relegation zone to within one point of ninth-place Everton in the space of three months. A top-half finish is definitely on the cards and that would be a miracle considering the resources Rafa has had to work with.
7.32pmEverton too look likely to finish in the top half, but that is not enough for a demanding fan base who not seen the chairman's ambitious spending matched by performances on the pitch. Allardyce did his job to drag Everton clear of trouble but already some Everton fans want a more ambitious boss.
7.34pmThe Toffees are 16 points worse off than at this stage last season, when they were seventh and within six points of the Champions League places, and they have also scored 21 fewer goals.
7.36pmEverton are not exactly finishing the season with the sort of momentum that would earn Allardyce a stay of execution. He is contracted until 2019 but there is a feeling that a change could be made in the summer, especially now that Marco Silva, the original choice to replace Ronald Koeman, is available.
7.38pmThe Blues are winless in three matches, although two of those have been against Manchester City and Liverpool. Last weekend's draw to relegation-threatened Swansea would have been a disappointment though, and in truth the Toffees were lucky to come away with a point.
7.40pmAllardyce better watch out because a defeat to Newcastle has not been a good omen this season...
👀 Here's a situation for Everton fans to mull over...
7.42pmHowever, if Everton are searching for more promising omens than they have several to clutch at, including the fact that they have won eight of their nine home league game this season against teams below them in the table. They have also won seven in a row against promoted opposition.
7.44pmAllardyce has lost only two of his 11 Premier League fixtures against Newcastle since leaving the club in January 2008, after only six months in charge, and Everton have won seven of their last eight Premier League fixtures against the Magpies, including the last four in a row without conceding a goal.
7.46pmAnd then there is this... (one particular volley stands out)
7.48pmHEAD TO HEAD: We have already touched on Everton's fine recent record against Newcastle, and it has been particularly good at Goodison Park. They have lost just one of 13 home encounters with United, and have scored at least two on each of their last five visits.
7.50pmWORLD CUP WATCH: There have been calls for Gareth Southgate to give Jonjo Shelvey a chance at international level, and he is one of the few English midfielders who has the progressive passing range to hurt defences. Can his end-of-season form put him in World Cup contention?
7.52pmElsewhere, Newcastle captain Jamaal Lascelles and Everton's Michael Keane have an outside shot of making the plane to Russia with Southgate likely to take five central defenders. Neither are in possession at the moment but might be called upon for cover if there are a couple of injuries.
Jordan Pickford is also in a battle with Jack Butland to establish himself as England's new number one.
7.54pmJust over five minutes until kickoff on Merseyside, which hosts an ever bigger match on the other side of Stanley Park tomorrow night as Liverpool play Roma in the first leg of their Champions League semi-final. Read our extensive match preview here.
7.56pmThe players emerge out of the tunnel at Goodison Park, which has been a happy hunting ground for Benitez. He has won on each of his last four visits here - once with Chelsea and three times with Liverpool.
7.58pmPREDICTION: Everton have a fine home record against teams below them in the table this season, but Newcastle are the side in form so I anticipate this being a close game. I reckon the Toffees might just pinch it 2-1 to climb above Leicester City and into eighth in the standings.
1 minKICKOFF: We are underway under the lights at Goodison Park, where Bobby Madley is our referee tonight...
3 minCHANCE! Walcott picks up the ball on the halfway line and drives forward with electric pace before trying to pick out Tosun. The ball eventually deflects into the path of the Turkish striker, who slashes horribly at a left-footed volley which drops wide. That is a decent early chance.
5 minEverton are not the same possession-obsessed side that they were under Ronald Koeman, when they kept the ball across the back for the sake of it, but they have had most of the ball early on here. Newcastle meanwhile haven't been afraid to go more direct with Slimani in the team.
7 minIdrissa Gueye catches Shelvey on the halfway line to give away a free kick. That will be a pivotal battle in the middle of the park tonight, where Everton should have a one-man advantage.
9 minNewcastle nearly counter from an Everton corner with Kenedy having the legs on Schneiderlin, but Pickford is quickly off his line to boot the ball into the stands in proper Peter Kay 'av it fashion.
11 minThis is Rafael Benitez's 100th game in charge as Newcastle manager. The Spaniard has won 48 of them, but perhaps more importantly he has won the hearts of an entire city, with his name being chanted from the visiting end at Goodison, despite the fact that his side haven't made a great start here.
13 minPickford has showed good awarness to sweep up a couple of promising Newcastle breaks already, and the former Sunderland man also has an advantage over Butland when it comes to distribution, although an attempted quick clearance to Bolasie goes over the winger and straight out of play.
15 minSpeaking of Bolasie, the Congolese winger is enjoying a run in the Everton team after over a year out with ligament damage. He still does not seem to be back up to full speed and that could mean he is in for a tricky evening as no full-back in the league is quicker than DeAndre Yedlin.
17 minBetween Tosun and Bolasie, Everton work the ball nicely across the edge of the box to Baines, whose cutback sets up the former Crystal Palace winger for a first-time shot with the side of his foot which is blocked by Lejeune, whose partnership with Lascelles has yielded three clean sheets in seven.
19 minThe hosts continue to be dominating possession without much penetration. Schneiderlin did knock a good pass over the top for Walcott but the forward could not bring the ball down.
21 minThe Magpies have not had many options in the final third so far and that shows as Perez chooses to take on an ambitious shot from 30 yards out which flies high over the crossbar.
23 minNewcastle's best method of attack seems to be on the counter with the pace of Kenedy and Perez, who nearly gets onto the end of a return pass from Slimani after starting the break himself.
25 minWalcott makes another good run in off the right wing, which is something Dummett needs to monitor more closely, but Dubravka is off his line quickly to collect Jagielka's 40-yard pass.
27 minThe former Arsenal man is involved again here as he slides a ball into the right channel for Tosun, who would have found Walcott with his clever return pass had Yedlin not come across from right back to provide crucial cover before a shot could be fired.
29 minWe had not much of Shelvey or Ritchie thus far, with Newcastle largely bypassing them to go direct. The latter gets to the right byline and stands up a cross which Slimani was threatening to meet at the back post before Pickford's intervention.
31 minSlimani hangs a hopeful ball up in the box and both Kenedy and Perez go for it at the same time. It is the Spaniard who makes contact but his tame poke rolls harmlessly along the floor to Pickford.
33 minShelvey seems to be getting frustrated at his lack of involvement. The midfielder has come a long way with improving his temperament in recent months so Benitez will hope he keeps his cool.
35 minCHANCE! The best chance of the game so far falls to Jagielka at the back post. The ball is recycled from a corner and Keane heads it across goal where Jagielka knocks it wide on the stretch from six yards.
37 minCHANCE! Now it is Newcastle's turn to squander a golden opportunity as Pickford's scuffed clearance falls to Perez, who would have sent Slimani through one-on-one with an out-of-position Pickford had he not badly overhit a simple pass under no pressure.
39 minDiame lines up a shot from long distance which might have tested Pickford had Keane not got a block in.
41 minAt this rate this will be the only thing that this game is remembered for...
🤖📺 The first ever virtual mascot...
Everton make Premier League history with a touch of class as their young mascot couldn't attend the game, but is able to watch the full thing from his iPad 👏#EVENEWpic.twitter.com/ncqPsAmPHe
43 minThe Toffees knock a couple of dangerous crosses into the box, firstly from Coleman and then from Baines, with Bolasie poised for a tap in at the back post before Dummett makes a clumsy interception.
45 minEverton are finishing this second half strongly and come forward again with Walcott, who is caught in two minds with a cross-cum-shot that drifts harmlessly behind as the whistle goes.
8.50pmThat was a half of football typical of an end-of-season game with little riding on it. Everton dominated the possession without creating many chances and Newcastle were equally uninspired.
8.52pmThe best of the few opportunities have fallen to the Toffees, with Jagielka slicing wide at the back post from a Keane knockdown and Tosun miscuing an early volley on his weaker left foot. Newcastle may have been one up though had Perez kept his composure to pick out Slimani.
8.54pmCan Newcastle improve in the second half to help Rafa to his best Prem run in nine years?
8.56pmMATCH STATS: Everton have had 68% of the ball but have failed to covert that into a single shot on target. They have had four corners and it has been from set pieces that they have arguably looked the most threatening.
8.58pmBENCH WATCH: Allardyce does not have much in terms of creative options on the bench. Calvert-Lewin would offer them a little more dynamism but they already have that in Walcott and Bolasie, on paper at least. Meanwhile Dwight Gayle is waiting in reserve for the visitors...
46 minKICKOFF: The second half resumes with both unchanged. Let's hope for an improvement!
48 minSHOT! The ball drops for Perez on his left foot but he stabs it wide under pressure from Jagielka.
51 minThis game gets the goal that it badly needed as Walcott ends his nine-match drought. Yedlin cannot clear his lines at the back post from a Rooney cross, and Walcott keeps his cool to wriggle past a couple of tackles and thrash the ball underneath the crossbar.
52 minSUBSTITUTION: A setback for Everton as Schneiderlin has to come off after being caught on the ankle by Ritchie in what seemed like a innocuous challenge. Talented oungster Tom Davies is on.
54 minAllardyce deserves credit for his role in the opening goal as he switched the wide players at half time. Had Bolasie still been on the left, I doubt he'd have had the composure nor the technique to finish as Walcott did.
56 minRooney sees space in front of him to run into and he tries to pick out the bottom corner with a 30-yard curler which Dubravka is happy to usher a few yards wide of his post.
58 minThe game is starting to look a little more stretched now, with Davies and Perez having found some space in between the lines in the last couple of minutes. He has been quiet thus far but this is where Shelvey can have a big impact with his passing range, if he has the movement in front of him.
60 minSUBSTITUTION: Everton make their second change as Calvert-Lewin replaces Bolasie who hasn't had the best of nights. That might mean a change of shape to 4-4-2, with Rooney shifted to the left which isn't going to improve his relationship with Big Sam whatsoever!
62 minSUBSTITUTION: Benitez responds with a change of his own as Gayle comes on for Slimani, who has not had the same impact from the start as he did from the bench last weekend.
64 minCLOSE! Gayle immediately has an opportunity to equalise for Newcastle as he hooks over the bar from close range, attempting an instinctive finish after Lascelles won a near-post flick on.
66 minGayle wants a free kick and action taken against Gueye after taking an arm in the face from the midfielder, but there was no intent to it, just an accidental flail after a 50-50 challenge in the air.
68 minA really dangerous cross from Kenedy forces Keane into a good clearing header at the back post.
70 minThe former Burnley defender is receiving treatment now after being caught by Gueye who again flew in recklessly when trying to win a header, catching his teammate with another stray arm.
72 minSHOT! Kenedy is starting to come into the game a little and he flies past Coleman and knocks in a cross which Perez heads straight down the throat of Pickford. It was a difficult chance but one that Slimani might have made a bit more of had he been on the pitch.
75 minYELLOW! Keane picks up the first booking of the game and it is for a cynical foul on Gayle, tripping the striker as he threatened to race into the area. Free kick in a very promising position for the Magpies.
77 minCLOSE! The set piece is in a perfect position for a left footer, and Newcastle have a specialist in Ritchie who strikes it sweetly but without the dip to drop it under the crossbar.
79 minSUBSTITUTION: That proves to be Ritchie's last action as Benitez brings on Josh Murphy on the right wing.
81 minThe pattern of the game has been turned on its head now, with Newcastle seeing most of the ball and Everton trying to hit them on the break through the pace of Walcott and Calvert-Lewin.
83 minSUBSTITUTION: It has not been Jonjo Shelvey's night tonight and he makes way for Mikel Merino, who was a cult hero at the start of the season but has lost his place to Diame.
85 minSUBSTITUTION: And now the final change from Everton as Niasse replaces Tosun in a case of fresh legs up top.
87 minPENALTY APPEAL! Newcastle want a penalty for handball against Jagielka, who was struck on a combination of his arm and torso as the ball richocheted around the era. Gayle was convinced but referee Bobby Madley waves away the appeals.
89 minThe hosts squander a chance to potentially wrap the game up on the break as Davies badly overhits a pass which would have released Niasse down the left. Allardyce and Ferguson are furious on the bench, but that's nothing compared to how they will be if Newcastle now grab a leveller!
90+1 minThere is going to be FIVE minutes of added time - not sure where the officials have got that one! The game might go longer now too after Bobby Madley has to take some time to defuse a hostile situation between Kenedy and Gueye which really started over nothing.
90+3 minLejeune has stayed forward as an emergency target man for Newcastle but Keane rises above the defender to win the header. He has had a decent game tonight, the England international, although he has been tested a little more since the spritely Gayle came on.
90+5 minBaines has taken a nasty cut to the face after being caught by the boot of Josh Murphy, completely unintentionally. He's had to leave the field and Davies is filling in as an emergency left-back.
90+6 minCLOSE! Murphy knocks a cross into a dangerous area - it may even have been sneaking into the top corner - and if it wasn't then Gayle was lining up to nod it home before Coleman put his body on the line to head the ball clear from virtually underneath his own crossbar. Brilliant defending.
9.58pmIt was far from a thriller but it is an important three points for Everton, who climb above Leicester into eighth and four points ahead of the Magpies in 10th. Newcastle's winning run ends at four but the Toon Army will still be pretty content to be miles clear of the relegation battle.
10.00pmThat's it from Goodison Park, but before you go you can read our match report on the action here. Let's hope for a bit more quality from the other half of Merseyside tomorrow as Liverpool face Roma in the Champions League, which you can follow with us at Sports Mole. Until then, goodbye.