Stevan Jovetic gave the Premier League champions the lead early in the second half but Jordan Henderson scored to haul the Reds level.
Jovetic then restored City’s advantage but Raheem Sterling’s later equaliser forced the pre-season friendly to penalties.
Aleksandar Kolarov, Daniel Sturridge, Yaya Toure and Jesus Navas all missed their spot-kicks, leaving Emre Can, Jordan Henderson and Lucas to win it for the Reds.
Here are highlights from the pre-season friendly in New York.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news