City moved up to second in the table, one point behind Arsenal, after rallying from a goal down thanks to a header from Vincent Kompany and a first-half stoppage-time strike from Negredo.
Liverpool keeper Simon Mignolet was at fault for Negredo's goal as he palmed his 18-metre effort up and into his own net. It was the ninth consecutive home game in all competitions in which the Spaniard has scored.
Third-placed Liverpool, who gave as good as they got in a pulsating game, went ahead after 24 minutes when Raheem Sterling rounded keeper Joe Hart and Philippe Coutinho slotted the ball into an empty net.
(Writing by Tony Jimenez; editing by Ed Osmond)
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