Bertrand’s Traore’s terrific finish had Dean Smith’s men leading at the break and on course for a first home league win over the Red Devils since 1995.
But United turned the game around when Bruno Fernandes, from the penalty spot, and Mason Greenwood struck in the space of four second half minutes.
Substitute Edinson Cavani then added a third before Villa saw Ollie Watkins sent-off late on.
The striker, booked in first half stoppage time for fouling Harry Maguire, was shown a second yellow for what referee Chris Kavanagh judged to be a dive when he looked to beat goalkeeper Dean Henderson to a through ball.
It added an unwanted sting in the tail for Villa, after a performance not without positives.
Dean Smith’s men were excellent in the first half, lively in attack and causing the United defence problems with their pressing.
But they handed the visitors a route back into the match when Douglas Luiz brought down Paul Pogba in the box seven minutes into the second half.
Fernandes stepped up to score from the spot against Villa for the third straight match and when Greenwood fired the visitors in front soon after, it always looked an uphill challenge for the hosts.
Cavani’s goal sealed a win for United which means their rivals Manchester City must wait a little longer before sealing the Premier League title.
Villa, without Jack Grealish for the 12th straight Premier League match, named the same XI which started the previous weekend’s 2-1 win at Everton.
United boss Ole Gunnar Solskjaer, meanwhile, picked arguably his strongest team for what was the visitors second of four matches in the space of eight days.
There were four changes from the team which had played the second leg of their Europa League semi-final against Roma on Thursday though it was one of those men who kept their place, Greenwood, who should have opened the scoring inside five minutes.
Marcus Rashford’s shot from the edge of the box took a huge deflection to loop invitingly into his path at the far post but instead of firing home he sent the finish back across goal, allowing Villa to clear.
Soon afterward roles were reversed when Greenwood’s mis-hit shot cannoned into Rashford’s heel six yards out, the striker unable to react quickly enough to steer the ball home.
United were made to pay for their profligacy. Though Villa were yet to carve out a clear-cut chance, the hosts had caused problems for the visitors with their high pressing.
And it led to the opener when Luiz won the ball in the final third and played a pass into the path of Traore. The winger’s attempt to roll Victor Lindelof initially appeared to have failed but the United defender was unable to clear and Traore thumped a left-footed finish high inside the far post, the one place goalkeeper Henderson had no chance of stopping it.
The visitors quickly went in search of a leveller but were unable to find one before the break, Martinez making his first big save of the match from Greenwood, with Konsa on hand to clear the loose ball.
Villa had chances at the end of the half and start of the second, with neither Watkins nor Anwar El Ghazi able to get enough power on their respective shots to seriously trouble Henderson.
They felt important moments when in the space of four minutes United turned the game on its head.
Villa only had themselves to blame. Pogba was heading away from goal when Luiz clumsily dived in, getting nowhere near the ball and making enough contact to send the France international to the ground. Fernandes sent Martinez the wrong way from the spot.
The second goal, meanwhile, was the consequence of questionable defending. Mings allowed Greenwood to escape his clutches too easily and from around 12 yards out the striker drilled a finish inside Martinez’s near post.
Villa looked a little shellshocked but were almost handed a route back in when a stretching Maguire could only deflect Matt Targett’s cross at goal, Henderson making a sharp save.
After Maguire was then forced off by injury, Smith threw caution to the wind by introducing Wesley and Keinan Davis off the bench. The latter got round the back of Lindelof but when he picked out Watkins, the latter’s shot was blocked.
With three minutes to go Cavani made the game safe for United when he headed home Rashford’s cross before Villa’s misery was complete when Watkins saw red moments later.
24 GOAL Bertrand Traore fires Villa in front, drilling a shot high inside the far post after good work by Douglas Luiz.
52 GOAL United level from the spot. Bruno Fernandes sends Emiliano Martinez the wrong way after Luiz brings down Paul Pogba.
56 GOAL Turnaround complete. Mason Greenwood turns Tyrone Mings before firing a shot inside Martinez’s near post.
87 GOAL Edinson Cavani heads home Rashford’s cross to seal the win for the visitors.
Villa (4-2-3-1): Martinez, Cash, Konsa, Mings, Targett, McGinn, Luiz (Ramsey 65), Traore, Barkley (Wesley 78), El Ghazi (Davis 78), Watkins Subs not used: Elmohamady, Hause, Nakamba, Chukwuemeka, Philogene-Bidace, Heaton (gk).
Man Utd (4-2-3-1): Henderson, Wan-Bissaka, Maguire (Bailly 78), Lindelof, Shaw, Fred, McTominay, Greenwood (Cavani 65), Fernandes (Matic 87), Pogba, Rashford Subs not used: Bailly, Mata, Telles, Willians, Van De Beek, Tuanzebe, De Gea (gk).