Everton went down to ten men after just 13 minutes when Idrissa Gana Gueye picked up a straight red for violent conduct after slapping teammate Michael Keane.
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Kiernan Dewsbury-Hall gave the visitors the lead 16 minutes later, and Man United offered very little going forward before the final whistle blew.
According to Opta, the defeat to Everton marked the first time Man United have ever lost to an opposition that went down to ten men at Old Trafford, winning 36 and drawing 10 of the previous 46.
United have now dropped down to tenth in the Premier League with just 18 points from their first 12 games and a zero goal difference.