The victory put them level on points and games played with champions and leaders Liverpool.
Manchester United trail their traditional rivals on goal difference with both teams on 33 points from 16 matches.
Liverpool travel to Southampton on Monday.
Manchester United stretched their unbeaten league run to 10 games as Bruno Fernandes capped another fine individual performance with a penalty kick.
This was after Bertrand Traore had cancelled out Anthony Martial’s opener for the home side.
The hosts had the upper hand in the first half and Martial forced an acrobatic save from Emiliano Martinez.
He later buried a superb diving header past the Aston Villa goalkeeper after Aaron-Wan Bissaka’s cross in the 40th minute.