Goals from Romelu Lukaku and Marcus Rashford were enough for Jose Mourinho's side to prevail in the International Champions Cup fixture in Texas, and they look on course to make an impression at the start of the new Premier League campaign.
As for City, they were taking part in their first friendly and while they were defeated in the United States, Pep Guardiola will take encouragement from the performance of 17-year-old Phil Foden, who was superb in his 74-minute showing in midfield.
City included both Ederson and Kyle Walker in their starting lineup after big-money moves from Benfica and Tottenham Hotspur respectively, and the former was in the action as early as the fourth minute to deny Ander Herrera from long range.
Guardiola's side responded through Raheem Sterling, who forced a solid stop out of David de Gea, and despite the occasion representing their first match of pre-season, they were competing well with a side who already had two games under their belt.
There continued to be opportunities at either end with Henrikh Mkhitaryan forcing a good save out of Ederson and Sterling once again getting a shot away after cutting inside onto his right foot.
City could have potentially taken the lead through Patrick Roberts had it not been for a last-ditch challenge from Chris Smalling, and United capitalised by moving ahead through Lukaku, who fired into the net from an acute angle after beating Ederson to a long ball.
Two minutes later, United doubled their advantage through Marcus Rashford, who benefitted from some positive play from Mkhitaryan before lashing the ball into the corner of Ederson's net.
Teenanger Foden was enjoying a fine debut for City and despite his shot being dealt with by De Gea, Guardiola would have been delighted with his first-half contribution.
At the break, City introduced seven fresh faces but it was United who carried on where they left off, and Rashford almost found the far corner of Ederson's net with an over-hit cross, only for the goalkeeper to get back and keep the ball out.
Soon afterwards, Lukaku came within inches of adding his second goal of the match with a thunderous effort from the edge of the area but despite beating the City goalkeeper, it struck the crossbar and rebounded clear.
Opportunities were being created as frequently as the first half, but United still looked like they could add to their lead and Paul Pogba should perhaps have done better with a shot which only hit the side-netting.
That represented the final action of a fairly entertaining game, but it is United who currently look the better prepared ahead of the new top-flight season, which begins in three weeks' time.
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