There were numerous thrilling passages of play as the two highest-scoring sides in the Premier League served up a Boxing Day cracker, with City coming from behind to overhaul their opponents and leave Liverpool fourth.
Philippe Coutinho broke the deadlock for the Reds in the 24th minute after a flowing move involving Luis Suarez and Raheem Sterling, but Vincent Kompany headed in a corner to equalise seven minutes later.
Alvaro Negredo then put City in front on the stroke of half-time after a swift counter-attack, although Simon Mignolet will have been disappointed not to have kept out the final shot after getting only a weak hand on the ball.
The second half was just as open but Liverpool were left to rue a series of missed chances as Sterling blazed over from close range and the excellent Joe Hart denied Glen Johnson.
The home side set out trying to exploit the weakness on Liverpool's left, where Aly Cissokho, the unconvincing on-loan Valencia defender, was making his first appearance since November 9 because of makeshift left-back Jon Flanagan's hamstring injury.
Jesus Navas almost made that pay when his looping header hit the outside of the post after he nipped in front of the Frenchman to meet a left-wing cross.
Kompany's header wide from a corner gave Liverpool a warning which they later failed to heed as City continued to probe and press.
By the time Negredo fired wide Suarez had already aimed a low free-kick straight at Hart as the tide started to turn.
Sterling should have had a clear run on goal after being picked out once by Suarez but play was incorrectly brought back by an offside flag, with television replays showing Sterling was at least a yard behind the last defender when the pass was made.
The same pair combined for the opening goal in the 24th minute when Suarez's ball over the top was destined for Sterling only for Coutinho to come in from the left and score from a narrow angle.
City's response was instantaneous as Yaya Toure went past three defenders with one turn only to be denied by the outstretched leg of Martin Skrtel.
The Slovakia defender has been singled out recently as the weak link at defensive set-pieces and while he was busy trying to grapple with Kompany the City captain had eyes only for David Silva's corner and glanced a header past Mignolet.
With City now holding the upper hand again Liverpool were by no means cowed and a brilliant move via Suarez and Sterling saw Coutinho force Hart into a smart save.
But City often catch opponents napping on the counter-attack and so it proved on the stroke of half-time when Mignolet failed to deal with Negredo's shot with the outside of his left foot from Navas' through ball as the visitors were cut wide open.
Negredo tried a similar effort early in the second half but this time the goalkeeper was better positioned.
The attacks continued at both ends with Sterling coming the closest with 17 minutes remaining when he diverted Suarez's inviting cross over from seven yards.
Hart also saved well from Johnson after the full-back's touch had let him down, while the England keeper also kept out a Jordan Henderson flick.
Late on Suarez appealed for a penalty with Joleon Lescott pulling at his shirt but as Skrtel had spent most of the match doing that to Kompany there was almost an argument for it being the same for both sides.
And City clung on in the finals stages to move up to second place, with Liverpool dropping from first to fourth in the closest of title races.