Stevan Jovetic struck a brace, either side of Jordan Henderson's crisp finish for the Reds, before Raheem Sterling equalised in the 85th minute.
After normal time finished 2-2, Brendan Rodgers' men were the better side in the shootout, claiming it 3-1 courtesy of two Simon Mignolet saves.
Jovetic opened the scoring in the 53rd minute after a defensive stumble from Reds midfielder Steven Gerrard, before Henderson's reply six minutes later.
However, the Montenegrin reinstated City's lead in the 67th minute, poking home an opportunistic effort to regain the lead for Manuel Pellegrini's outfit.
Sterling struck late in regulation with a well-taken finish, before City crumbled in the shoot-out, as each of Aleksandar Kolarov, Yaya Toure and Jesus Navas all failed to convert from the spot.
Jovetic was influential for the Premier League champions early, linking effectively with strike partner Edin Dzeko.
Dzeko put the ball in the back of the net in the 26th minute, however the Bosnia-Herzegovina international was correctly flagged for offside.
City had the most chances in the opening 45 minutes, but arguably Liverpool had the best opportunity to score - when Rickie Lambert's point-blank range header was kept out by City custodian Willy Caballero.
The former Southampton striker was at the back post for Henderson's chipped cross, but Lambert's header went straight at the chest of Caballero - whose reflex save kept the game scoreless.
The contest continued in its attacking nature with Liverpool substitute Jack Robinson almost opening the scoring in the 50th minute, only to be denied by fellow sub and City custodian Joe Hart, who rushed off his line to clear the danger.
But three minutes later, Navas danced around Robinson on City's right wing, and delivered a cross into the goalmouth.
Gerrard's attempt to block failed, as he let the ball through his legs, with Jovetic swooping on the remnants to put City ahead.
Henderson's finish brought the partisan Liverpool crowd to life, completing fine lead-up work from Sterling and Daniel Sturridge to mark City's sheet for the fifth straight match in pre-season.
Jovetic was on hand again to cap a man-of-the-match performance, incidentally blocking Kelechi Iheanacho's strike but swooping on the loose ball to poke City ahead.
Sterling showed his class to finish with less than six minutes of normal time remaining.