City, in third place, stayed a point ahead of the Merseysiders with a game in hand thanks to Sergio Aguero's equalising goal.
Knocked out of the Champions League by Monaco in midweek, City fell behind when full back Gael Clichy conceded a penalty six minutes after halftime and James Milner scored from the spot against his old club.
Liverpool, who had come into the game more after a slow start, were pegged back 18 minutes later when Aguero scored from Kevin de Bruyne's fine low cross.
De Bruyne then hit a post and Adam Lallana missed badly for Liverpool in an exciting finish.
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