Two goals from Wayne Rooney moved him into fourth place ahead of Frank Lampard on the list of all-time Premier League scoring leaders. Juan Mata and Javier Hernandez added a goal apiece.
The win was a huge confidence-builder for David Moyes' struggling side, who will face holders Bayern Munich in the first leg of their Champions League quarter-final tie on Tuesday.
The result moved United to within two points of Tottenham Hotspur in sixth and kept alive their outside hopes of a Champions League spot.
It started badly for the hosts, however, as an Ashley Westwood free-kick gave Villa the early lead, but a brace from Rooney - a header and a penalty - had them in front at the break.
Old Trafford erupted on 57 minutes as Mata scored his first Premier League goal since last May, with an assist from Marouane Fellaini, an alumnus of Moyes' old club Everton. The strike was the Spaniard's first for his new team since his move from Chelsea in January.
Javier Hernandez put the icing on the cake with an injury-time tally to make it 4-1
United came into the match having suffered home losses against Manchester City and Liverpool in the last fortnight, and a 2-2 draw against cellar-dwelling Fulham has also been a blot on their home record.
The return of rugged captain Nemanja Vidic from a two-match provided a timely boost and helped settle the side down in the back.
United have now won their last seven league matches against Villa, including a 3-0 victory at Villa Park in December.
Villa were hammered 4-1 by Stoke City last weekend, but they still believe they can finish the season in the top half of the table. A 1-0 win over leaders Chelsea earlier this month and a 2-2 draw at Liverpool in January are proof that the side has potential.