Managers Jurgen Klopp and Jose Mourinho have clashed in recent days over spending, but it was the Reds who came out on top.
Goals from Sadio Mane, Daniel Sturridge, Sheyi Ojo and Xherdan Shaqiri on his debut gave Klopp’s men victory in Michigan.
Andreas Pereira scored a free-kick for United but could not stop Liverpool making it two wins from three in the tournament and completing a Manchester double after their 2-1 win over Premier League champions City on Thursday.
The friendly fixture was played in front of 101,254 fans in Ann Arbor.
United continue their International Champions Cup campaign against Real Madrid in Miami on Wednesday.
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The Red Devils then face Bayern Munich in a friendly at the Allianz Arena the following Sunday.
Liverpool round-off their pre-season preparations with a trip to Dublin to face Napoli on Saturday, before hosting Torino at Anfield on August 7.
Meanwhile, new United signing Lee Grant has no intentions of settling for the role of third-choice goalkeeper at Old Trafford next season.
“I’m old enough and ugly enough to understand the role I’m coming in to do,” he said of his £1.5million move from Stoke.
“I’m at a club that has the best goalkeeper in the Premier League, also that has Argentina’s No1 keeper and there are also fantastic young keepers in the building and out on loan.
“I know what I have to contend with but I’m confident in myself, I’m settled with my own role and I’m also certain I can offer something to the club.
“My job is just to hold up my end of the bargain. My role is to perform at a high level and conduct myself in the correct manner.
“That means training correctly, playing correctly when you get the opportunity and, if that gives the manager a choice to make, then that’s my job.”