Martin Skrtel gave Liverpool the lead with a powerful header from a Steven Gerrard corner in a first half in which Brendan Rodgers' team edged the defending champions.
Yaya Toure equalized for Roberto Mancini's side in the 63rd after Pepe Reina failed to claim a cross that Martin Kelly could not control, allowing Toure to finish from close range.
Luis Suarez restored Liverpool's lead with a perfectly executed low free kick into the corner of Joe Hart's goal.
Skrtel was at fault for City's second with an under-hit pass back toward Reina, which Carlos Tevez ran on to, rounding Liverpool's goalkeeper and slotting into an empty net.