Philippe Coutinho's second goal of the season put Brendan Rodgers' side in front after 24 minutes in the battle of the Premier League's two most free-scoring sides at the Etihad Stadium.
Vincent Kompany equalised just seven minutes later and Simon Mignolet was at fault for Alvaro Negredo's 14th goal of the season that put City in front on the stroke of half-time.
City are now just a point behind leaders Arsenal in second place and have won six of their last seven top-flight games, while Liverpool sit three points behind Arsene Wenger's side in fourth.
Liverpool soon got into their stride and were in front after 23 minutes when Sterling got on the end of Luis Suarez's exquisite flick then rounded Joe Hart and Coutinho nipped in front of the winger to slot into the empty net from a tight angle.
City were a constant threat and it took them only seven minutes to get back on level terms as Kompany rose to head down David Silva's corner and Joe Allen was unable to clear on the line.
Negredo was not to be denied in first-half stoppage, though, as Mignolet could only palm the striker's left-foot strike behind him and into the net after Navas had picked out his Spain team-mate.
Liverpool started the second half on the front foot and Kolarov was almost made to pay for being far too casual in the area when Suarez robbed him, but the Uruguayan's shot hit Jordan Henderson and the defender's blushes were spared.
Negredo rose to meet a Silva corner but headed straight at Mignolet. Liverpool continued to ask questions of the City defence and Glen Johnson's touch let him down after Lescott's attempted clearance fell nicely for him.
