The Reds secured all the points late on, however, when Philippe Coutinho found the bottom corner from outside the box.
Here, Sports Mole dissects the 90 minutes of action between the two Premier League rivals.
On target: 4
On target: 5
Was the result fair?
Liverpool were much the better team in the first period this afternoon, but City's second-half display should have earned them a point at Anfield. When the away side levelled at 2-2, it appeared that they would go on to claim all the points. However, a horror mistake from City skipper Vincent Kompany allowed Coutinho to find the bottom corner from outside the box. Both sides impressed with their attacking football and on the balance of play, a point apiece would have been a fair reflection of the events on Merseyside.
Liverpool have blown teams away at Anfield this season - especially in the first period - and it appeared that would be the case once more when they moved two goals ahead after 26 minutes. It was frightening football from the Reds, who completely smothered City in all areas of the field. However, a slow start to the second half allowed Manuel Pellegrini's side to find their way into the contest. Liverpool's defence has been far from watertight this season and at 2-2, it appeared that they would be on the end of a defeat due to serious pressure from the visitors. However, the league leaders found another gear in the latter stages to secure what could be a vital three points in the context of the title. As it stands, they sit five points clear of second-place Chelsea and seven clear of third-place City, who have two games in hand.
It was hardly the ideal build-up to the match for City, with skipper Kompany a serious doubt after picking up an injury in training. The Belgian started, but it was clear that he was not fully fit. It got worse early on when Sterling opened the scoring for Liverpool, before Yaya Toure was forced to leave the field with a knee injury. A second Liverpool goal left Pellegrini's side with a mountain to climb, but they showed incredible character in the second period to respond against a side that has simply rolled teams over at Anfield this season. At 2-2, they were in control and looked as if they would go on to claim all three points, but a mistake from Kompany handed Liverpool a vital win. They are far from out of the title race, but are facing the prospect of being without Kompany and Toure for the remaining games of the season.
Sports Mole's man of the match
David Silva: Silva finished on the losing side this afternoon, but it took nothing away from the City attacker's performance. In truth, the Spaniard struggled to influence proceedings in the first period - as did a number of his teammates - as Liverpool dominated for long spells. However, the former Valencia winger was just sensational in the second. It was his strike that made it 2-1 in the early stages of the half, before his cross was turned into the Liverpool net by Johnson for 2-2. The classy 28-year-old did not deserve to be on the losing side at Anfield.
City skipper Kompany was an injury doubt in the build-up to the match and while overall the centre-back had a solid match, he cost his side in the latter stages. It appeared to be a straight-forward clearance for the Belgian inside his own box, but he sliced a high ball straight into the path of Coutinho, who curled one into the bottom corner for Liverpool's third. It was clear that the defender was struggling in the latter stages with his knee, but Pellegrini kept him on the field.
City had a strong case for a penalty in the first period when Mamadou Sakho brought Edin Dzeko to the ground with a clumsy challenge, but referee Mark Clattenburg was not interested. That was just the start of what was a busy afternoon for the English official. City had another strong penalty claim late on when Skrtel handled inside his own box, but once more no decision was forthcoming. The Blues will also feel that Liverpool forward Luis Suarez should have been sent from the field in the second period after diving just outside the penalty area. A red did arrive for the home side late on following a horror challenge from Jordan Henderson on Silva, but it was too late to boost City's chances. That said, despite a number of what could be described as errors, Clattenburg showed his incredible fitness levels throughout the 90 minutes to keep up with events and contributed to the end-to-end nature of the contest by not stopping play unless deemed absolutely necessary.
Liverpool: Liverpool will attempt to continue their title charge when they travel to out-of-form and relegation-threatened Norwich City next weekend.
City: City must bounce back quickly in the Premier League when they welcome basement outfit Sunderland to the Etihad on Wednesday evening.