A thrilling International Champions Cup clash ended with a penalty shoot-out after both sides took the game to each other in front of a bumper crowd in New York
Stevan Jovetic scored twice, once either side of a fine Jordan Henderson strike, while Raheem Sterling equalised late on to force spot-kicks.
Aleksandar Kolarov, Daniel Sturridge, Yaya Toure and Jesus Navas all missed from the spot, leaving Emre Can, Jordan Henderson and Lucas to win it for the Reds as Kelechi Iheanacho bagged a consolation.
The match started at a good pace; Jovetic and Edin Dzeko combined to cut open the heart of the Liverpool defence early on, but the Montenegro striker was forced too wide, and after recovering to put the ball through Martin Kelly's legs he went to ground too easily and the move fizzled out.
Jovetic then put a free header from a corner over the bar, before Coutinho fired a low shot just wide for Liverpool at the other end.
Rickie Lambert should have opened the scoring on 15 minutes but his close-range header from Henderson's cross was straight at Willy Caballero.
Bruno Zuculini then found himself through on goal following some fine interplay in the midfield, but he went for an ambitious chip from outside the area which was easily fielded by Brad Jones.
City thought they had taken the lead on 25 minutes but Dzeko was marginally offside, so his low strike was ruled out.
After the break Jesus Navas, impressive throughout, got the better of half-time substitute Jack Robinson on City's right-hand side only for his cross to be cut out by Sebastian Coates. Robinson recovered to head away the resulting corner, but was then beaten again by Navas on the right, allowing the Spaniard to put in a cross which evaded Steven Gerrard's attempts to clear and allowed Jovetic to poke home from close range.
City could have had a penalty shortly afterwards when Robinson handled a Jovetic chip, but Liverpool used that stroke of luck to their advantage and quickly equalised.
Raheem Sterling, the star after coming on at the break, ran straight at the heart of the City defence and picked out Sturridge. The striker was well tackled by Kolarov, but the ball fell straight into the path of the on-rushing Henderson, who stroked past Joe Hart with power and precision.
Zuculini had a great chance to give City the lead again, but the youngster somehow fired his shot against the crossbar from five yards out.
But Jovetic did make it 2-1 when Iheanacho's low shot was blocked by Coates, which allowed the Montengro striker to instinctively toe-poke home.
The Reds had a good chance to level when Sterling got in behind the City defence, but after he cut the ball back to the edge of the area Coutinho could only slide his shot wide of the post.
Sterling got the equaliser five minutes from time. Sturridge did well to hold the ball up in the left-hand corner before picking out Lucas on the edge of the box. The Brazilian played it first time to Sterling, who took the ball into the box and slotted past Hart with aplomb.
The England winger then looked to have won it with anastonishing effort from the left side of the box which flew into the top corner, but he was flagged offside.
Penalties followed a thrilling second half, but the first three kicks were missed in barely credible fashion.
Kolarov blazed his spot-kick, the first of the night, well over the bar, only for Sturridge to step up next and produce a carbon copy.
Even Yaya Toure saw his effort saved by the legs of Simon Mignolet, before Emre Can slotted his home. Mignolet saved again from Jesus Navas, as Jordan Henderson gave his side a 2-0 lead in the shoot-out.
Iheanacho produced an excellent penalty to get his side off the mark, but Lucas converted next to give Liverpool the victory, and two points towards their International Champions Cup campaign.
The Reds are now top of their group by one point, and could even face Manchester United in the final on Monday if results go both sides' way.