The visitors broke the deadlock after less than three minutes when Jamie Vardy tapped into an empty net following a defensive error, and Liverpool failed to make the most of a string of chances to equalise before half time.
However, Mohamed Salah came to the rescue once again for the Reds as his second-half brace turned the game around and handed Liverpool a victory which lifts them four points clear of the chasing pack in the race for a top-four spot.
Find out how all of the action unfolded courtesy of Sports Mole's minute-by-minute coverage below.
This is the final match of 2017 for both of these teams, and they will be looking to bring a rollercoaster year to a positive end here on Merseyside. Liverpool know that anything other than a win could see them end 2017 outside the top-four places, but Leicester will be desperate to arrest their recent dip in form, so this one should be a very intriguing contest.
We will have a closer look at both teams shortly, but first let's check out the team news...
Well, the headlines as far as Liverpool are concerned surround their 'Fab Four', who all start this afternoon despite some reports that Klopp may look to rotate again.
Salah, Coutinho and Firmino all started last time out, but Sadio Mane returns to the lineup this afternoon to bring Liverpool's devastating attack up to their fill complement. Alex Oxlade-Chamberlain - who was also on the scoresheet against Swansea City - is the man to make way.
Throw Mane into the fold as well and that statistic improves even more, and all of them come into this match in fine form. Salah unusually didn't score against Swansea but still helped himself to two assists, Coutinho opened the scoring and Firmino helped himself to a brace to make it four goals in his last three games now.
Perhaps the most notable change aside from Mane's return is that of Loris Karius, who gets a rare Premier League start between the sticks as Simon Mignolet drops to the bench. Karius has mostly been limited to Champions League action so far this term, but he gets his chance domestically here.
Alexander-Arnold in particular may feel a little hard done by having scored his first Anfield goal during the rout of Swansea, but Gomez remains just above the youngster in the pecking order and was always likely to return today. Can continues in the middle of the park, meanwhile, with captain Jordan Henderson still sidelined by a hamstring injury.
With Simpson having earlier limped off in that match - and now expected to miss more than a month of action - Leicester were forced to play Dragovic at right-back last time out against Watford, but he drops to the bench as Amartey returns today.
There are also returns for Iborra and Gray further forward as King is also left out of the squad, while Okazaki only makes the bench for this one. Mdidi, Mahrez and Alrighton all retain their places in that midfield.
There will most likely be some rumours linking him with a move away from the King Power Stadium once the transfer window reopens on Monday, but his recent displays have not suggested that he has one eye on a move away from the Foxes, despite numerous reports claiming that he was eager to leave during the summer.
Vardy tends to thoroughly enjoy himself against Liverpool, scoring more goals (six) and being directly involved in more (seven) than against any other opponent in the Premier League. Indeed, Vardy has been personally responsible for six of the eight goals Leicester have scored against Liverpool during their last four Premier League meetings.
Liverpool have never spent so much on a player, and no team has ever spent so much on a defender, but whether Van Dijk is the only answer to Liverpool's well-known defensive issues remains to be seen. It is a big ask for the Dutchman to single-handedly sort out the problems, with the common consensus being that Liverpool also need a new goalkeeper and defensive midfielder at least.
Across all competitions Liverpool have kept 11 clean sheets in their last 16 home games, conceding only seven goals in that time. In contrast, they have conceded 27 goals in their last 16 away games, keeping only four clean sheets in the process.
Away from home, though, Liverpool have conceded 20 goals - the joint-third highest tally in the league - keeping only two clean sheets compared to seven in front of their own fans.
The biggest problem for Liverpool in front of their own fans has been drawing games; Klopp's side are one of only two teams yet to lose a home league game this season, but they would still only be sixth in the table if just home form counted having drawn half of their 10 matches here at Anfield this season.
Even so, Liverpool are still unbeaten at Anfield across all competitions this season - stretching back 14 games, including 12 in the Premier League, since April. They had drawn three in a row in the league before Tuesday's 5-0 rout of Swansea, though.
The Reds last went 12 league games without defeat in March 2015 and a win today would not only hand them back-to-back victories for the first time since the beginning of the month, it would also send them four points clear of Arsenal and Tottenham Hotspur, with neither in action today.
Liverpool's tally of 75 goals from 29 games across all competitions this season is their highest-ever total at this stage of a campaign as a top-flight club, and one goal today would ensure that record remains after 30 games too.
Of all the teams in Europe's top five leagues, only Manchester City (77) and Paris Saint-Germain (89) have scored more goals this term.
Liverpool are more than capable of blowing most teams away with a flurry of goals, but Leicester - and most other teams, for that matter - will know that if they are still within touching distance heading into the closing stages then Liverpool are also perfectly capable of gifting points to the opposition.
Indeed, Leicester have now lost three of their last four games - including a penalty shootout defeat in the EFL Cup - having lost only one of the previous 12 before that.
In the Premier League their slump has been even more pronounced, having taken only one point from the last nine on offer following a run of four consecutive victories before that.
Another defeat today would condemn them to successive league losses for the first time since September following that reverse at Vicarage Road on Boxing Day.
Leicester should be relatively safe from being dragged into that if they continue as they have been doing under Puel, currently sitting 10 points clear of the bottom three and only 11 off the top four.
However, the Foxes did see their seven-game away unbeaten streak come to an end at Watford on Boxing Day, and another defeat today would see them fall to two on the bounce for the first time since the opening two of the season - against Arsenal and Manchester United.
Leicester do have a very tough run coming up on the road too, with Liverpool, Chelsea, Everton and Manchester City to come in their next four away games.
Puel himself has a good record against Liverpool, though, avoiding defeat in all six of his previous meetings with the Reds and already having won at Anfield with both Lyon and Southampton. The last manager to win an away game at Anfield with three different clubs was Martin O'Neill.
This fixture usually provides goals - 14 in the last three Premier League meetings, to be precise - and I can't see that changing today. Puel has a reputation for being more solid at the back than some of his Leicester predecessors, but Liverpool's attack and Leicester's counter should turn this into an entertaining game. I'm going for a Liverpool win, though.
SPORTS MOLE SAYS: Liverpool 3-1 Leicester
The first saw Leicester run out 2-0 winners in the EFL Cup, but Liverpool had . quick shot at revenge when they played them in the Premier League four days later. That proved to be another entertaining contest which Liverpool eventually won 3-2 courtesy of goals from Salah, Coutinho and Henderson. Okazaki and Vardy were on target for Leicester.
Leicester have won three of the last five competitive meetings following a winless run of seven in a row for them before that.
Firmino helped himself to a brace in that match, with Mane and Lallana also on the scoresheet while Vardy - of course - got his customary goal as a consolation.
LIVERPOOL STARTING XI: Karius; Gomez, Matip, Lovren, Robertson; Can, Milner, Coutinho; Salah, Firmino, Mane
LEICESTER STARTING XI: Schmeichel; Amartey, Maguire, Morgan, Fuchs; Mahrez, Iborra, Ndidi, Albrighton, Gray; Vardy
Matip's pass out from defence gifts possession back to Leicester in a dangerous area, and Iborra immediately releases Mahrez in the box. The Algerian only has the keeper to beat but unselfishly squares to to Vardy for a simple finish. What a start for the Foxes, but a nightmare one for Liverpool!
22 - Since August 2014, nobody has scored as many goals in the Premier League against 'big six' opposition as Jamie Vardy (22 goals in 41 apps). Prey.— OptaJoe (@OptaJoe) December 30, 2017
The Foxes opened the scoring early on, but from that point on it was been one-way traffic for Liverpool. The Reds have created chance after chance, but are yet to find a way past Schmeichel this afternoon.
It was another defensive error which led to the goal - and with new signing Van Dijk watching on too - as Matip gave possession away in a dangerous position. Iborra quickly pounced on it and played the ball through for Mahrez, who in turn teed up Vardy for a tap-in.
The Egyptian winger had a glorious chance just a few minutes after Liverpool had fallen behind only to place his finish wide of the target when he really should have scored, and he also failed to hit the target with another one-on-one chance later in the first half.
Leicester did tighten things up at the back towards the end of the half, with Liverpool's openings drying up after the half-hour mark, but the Reds have certainly had enough chances to be leading this one.
He was wasteful in the first half, but he makes no mistake here! Mane releases the winger with a superb back-heel through-ball, and Salah then takes him time to invite a couple of tackles inside the area before stroking his finish home.
21 - Mohamed Salah has been directly involved in 21 goals in 21 Premier League appearances for Liverpool this season (16 goals, 5 assists). Ridiculous.— OptaJoe (@OptaJoe) December 30, 2017
Maguire was far too tight to Salah, who showed good skill and strength to roll his man and his finish was unerring too. What a season that man is having.
The Foxes took the lead after only three minutes and may have begun to believe that it would be their day when Liverpool missed a string of chances, but Salah's second-half double ensures that Liverpool will begin 2018 in the Champions League places.
Thank you very much for joining Sports Mole for today's match as Liverpool ensure a winning end to 2017 courtesy of Mohamed Salah's brace. I will leave you with our match report, and be sure to stick around for reaction too. From me, though, it is goodbye for now!