Manuel Pellegrini's side made it an impressive nine out of nine - with 37 goals scored - to move into second place behind Arsenal as the Reds, who were looking to regain top spot, slipped to fourth after a 2-1 defeat.
However, had Raheem Sterling's effort not been wrongly ruled out for offside before either side had scored - and goalkeeper Simon Mignolet not made a hash of Alvaro Negredo's winner - Brendan Rodgers' side could well have got much more out of this game.
As it was they contributed much to an enthralling match which was billed as a test of their title credentials.
That may still be something of a distant dream, considering Rodgers was forced to name 19-year-old reserve team defender Brad Smith in his squad for the first time, but it did plenty to suggest their top-four challenge is alive and well.
City, of course, remain favourites for the title and their home form will be a major factor in achieving that but for all their goals what was just as impressive about this performance was the way Kompany and Joleon Lescott kept the Premier League's top scorer Luis Suarez on a tight leash in terms of chances.
Philippe Coutinho's opener sparked the home side into life and after Kompany had equalised from a corner Negredo's 14th goal of the season ultimately clinched another three points.
No team have scored more at home in the Premier League than City this season while Liverpool were the top flight's top scorers on the road so the portents were good and the first half did not disappoint as both sides attacked each other freely.
City had the better of the first and last 15 minutes with their visitors enjoying the middle third.
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 Joe Hart as the tide started to turn.
Sterling's diagonal run from the right had already been picked out once by Suarez without success but when the Uruguay international found the youngster again and he did not make the same mistake, going around Hart to score into an empty net.
Play was brought back by an offside flag but television replays showed Sterling was at least two yards behind the last defender when he was played through.
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 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.
Late on Suarez appealed for a penalty with 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.