Tyrone Mings struck just two minutes after Victor Lindelof had given United a 64th-minute lead, the Swede heading home at the far post for just his second goal for the club.
Earlier, Tom Heaton deflected Marcus Rashford's header into the back of the net to cancel out Jack Grealish's whipped opener for the impressive visitors.
Watch the highlights from the game in the video above, and see reaction from manager Ole Gunnar Solskjaer and captain Harry Maguire below.