Stevan Jovetic bagged a brace for Premier League champions Manchester City but Jordan Henderson and Raheem Sterling replied for Liverpool, who finished second last season.
Simon Mignolet then pulled off a pair of saves in the shoot-out to give the Reds victory in front of a crowd of 49,653.
The win put Liverpool on top of Group B in the International Champions Cup and they move on to play AC Milan on Saturday, with the possibility of a final against Manchester United to follow.
The Yankee Stadium spectators were served up an entertaining encounter between the top two teams in England last season and City new boy Willy Caballero produced a great save in the first half to keep out a close-range Rickie Lambert header.
At the other end, Brad Jones saved a low Jesus Navas effort and Edin Dzeko had a goal ruled out for offside.
Manchester City took the lead in the 53rd minute when the lively Navas made progress down the right and sent over a low cross which Jovetic converted at the near post, after Steven Gerrard was unable to clear.
But Liverpool responded just six minutes later, Henderson conjuring up a delightful curling finish after the ball ran loose when Sterling tried to find Daniel Sturridge.
Jovetic (67) quickly restored City’s lead, poking the ball past Mignoelet after a deflected shot fell perfectly for him.
However, Liverpool pressed strongly in the closing stages and, with just five minutes left to play, Lucas cleverly set up Sterling with a cushioned pass and the England man’s excellent finish set up spot-kicks.
City were far from clinical with their penalties, Aleksandar Kolarov punting their first over the bar, although he was reprieved when Sturridge did likewise.
But Mignolet then saved well from Yaya Toure and Navas, while Emre Can and Henderson converted.
City finally found the net when youngster Kelechi Iheanacho stepped up but Lucas then sent Joe Hart the wrong way to win it for Liverpool.