The tit-for-tat tussle saw Liverpool regain top spot courtesy of a convincing 5-0 win over Huddersfield Town on Friday night, only for City to wrest it back from their grasp with a gritty 1-0 triumph over Burnley on Sunday - the 30th change of leadership this season.
Whereas neither title contender is showing any sign of slipping up, it is quite the opposite in the top-four race as a second consecutive weekend passed without any of the contenders managing to win.
Tottenham Hotspur saw their perfect start to life at the new stadium ended by London rivals West Ham United, Arsenal were well beaten by Leicester City and Manchester United played out a 1-1 draw with Chelsea to leave the Blues still in control of the final Champions League spot.
At the other end of the table, Cardiff City's survival hopes took a hammer blow as they were beaten by relegated Fulham - a result which helped secure safety for Southampton coupled with their topsy-turvy 3-3 draw against Bournemouth.
It was an important weekend in the battle for seventh place too, with Wolverhampton Wanderers getting revenge over Watford for their FA Cup defeat and Everton being held to a goalless stalemate by Crystal Palace.
Here, Sports Mole selects its Premier League team of the week for gameweek 36.
Fulham's defensive work has not won many plaudits this season - understandably considering that they have conceded 76 goals - but it is now three wins and three clean sheets in a row for the Cottagers and at times it felt as though it was Sergio Rico against the world during Saturday's win over Cardiff.
The Spaniard made eight saves in the second half alone to earn the gloves ahead of Lukasz Fabianski, who was also impressive in West Ham's win at Spurs.
Liverpool were the big winners of the weekend as they hit five past Huddersfield, and as a result they dominate this week's XI with six players - three of which come in defence. Unsurprisingly the newly-crowned PFA Players' Player of the Year Virgil van Dijk is among them having had more touches and made more passes than any other player in the win, also playing a big role in Liverpool's second goal.
While Van Dijk has improved Liverpool's defensive solidity beyond recognition, the full-backs offer a huge threat going forward too and that was evident again at Anfield. The assist battle between Andrew Robertson and Trent Alexander-Arnold has been a feature of the season and Robertson edged further in front with two to Alexander-Arnold's one on Friday night - including a record-equalling 11th of his Premier League campaign.
Aaron Wan-Bissaka, Ricardo Pereira, Aymeric Laporte and Dejan Lovren deserve honourable mentions at the back, but Issa Diop is the man who raids the Liverpool party in defence courtesy of a titanic display at Spurs which saw him make more clearances, interceptions and blocks than any other West Ham player to keep their hosts at bay - not to mention almost scoring an incredible solo effort too.
Arguably the game of the weekend came at St Mary's, and it is perhaps harsh that only one of the players from that six-goal thriller makes this week's XI. Pierre-Emile Hojbjerg is the man to make the cut, having registered an assist as well as a game-high eight tackles in the middle of the park.
Leicester could have contributed either Youri Tielemans or James Maddison to this week's team after both put in fine performances in the win over Arsenal, but it is the latter who gets the nod for us having helped to pull the strings as well as getting an assist for Tielemans's goal.
Bernardo Silva and Georginio Wijnaldum were also considered in midfield, but Wijnaldum's clubmate Naby Keita needed a spot following his goal after just 15 seconds against Huddersfield - Liverpool's quickest ever in the Premier League. Keita's all-round performance was impressive too as he continues to find his best form towards the end of the campaign.
While Liverpool's full-backs are in friendly competition for the title of assist king, Sadio Mane and Mohamed Salah are vying for the Golden Boot after both netted braces to take them on to 20 and 21 goals respectively. Mane should have had a hat-trick of headers after hitting the post with a good chance, but Huddersfield could not live with him while Salah added an assist to his two goals to produce arguably the standout performance of the weekend.
Sergio Aguero looks set to rival that duo for the Golden Boot after he squeezed a vital goal over the line against Burnley, but he misses out on this week's team along with the likes of Eden Hazard, Ryan Babel, Michail Antonio, Diogo Jota and two-goal Callum Wilson.
Wilson is perhaps the most unfortunate not to be included, but his late missed chance to win the game for Bournemouth gives the edge to Jamie Vardy, who also helped himself to two goals against Arsenal as he extended his fine record against the Premier League's big boys.