With the game petering out to a goalless draw, Kortney Hause headed home in the 88th minute to seal the victory for the visitors.
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United were given the chance to equalise in stoppage time when referee Mike Dean pointed to the spot after Edinson Cavani's header was adjudged to have struck Hause's arm, but Fernandes hit his effort way over.
Villa boss Dean Smith was frustrated with the penalty award despite his side's win. He said: "We caused them problems from set-pieces and we get that goal and want to see the game out then, but inevitable when we play Man United we give a penalty away.
"Extremely harsh -- I'm not sure where he's meant to put his arm and probably justice was done. They'll enjoy that one and certainly our fans will because it's a long time coming."
Cristiano Ronaldo was back in the starting lineup, having been among the first-team players left out of the Carabao Cup third-round defeat to West Ham United, but failed to find the net for the first match since his return.