The Red Devils dominated the early exchanges at Villa Park, but Dean Smith's side eventually grew into the game and broke the deadlock in the 24th minute through Bertrand Traore, who beat Victor Lindelof before firing home into the top corner.
In a mirror image to their meeting at Old Trafford earlier in the season, Villa's Douglas Luiz gave away a penalty for a foul on Paul Pogba in the 51st minute, and Bruno Fernandes calmly slotted home to level the scores early in the second half.
Things went from bad to worse for Villa as Ole Gunnar Solskjaer's side grabbed a second on minute 56, with Mason Greenwood turning away from Tyrone Mings before firing home into the bottom corner, and things started to get tetchy as Villa searched for an equaliser.
Smith's men pressed for a second in the dying embers after United lost Harry Maguire to injury, but it was United who had the last laugh as Edinson Cavani came off the bench to head home and wrap up the three points for United, while Ollie Watkins was sent off less than two minutes later during a miserable second period for Villa.
Solskjaer's side remain second in the table - 10 points behind Man City with a game in hand - while Villa stay 11th, two points adrift of a top-half finish.
United only have 48 hours to recover before they face Leicester City on Tuesday night, while Villa prepare to welcome Everton to the West Midlands on Thursday evening.
7th min: Anwar El Ghazi lets fly from distance and the ball sails wide of the goal.
9th min: Another Man United attack ends with Fred getting a speculative shot away, but Martinez comfortably gathers.
16th min: A ball over the top from Pogba finds Rashford, who proceeds to set up Bruno Fernandes inside the area, but he cannot set himself for the shot in time.
21st min: Mason Greenwood nearly picks out Rashford at the far post, but Matt Targett makes a vital interception just in time.
24th min: Villa draw first blood after winning the ball back. Douglas Luiz finds Bertrand Traore, who manages to evade the futile attempts of Victor Lindelof to dispossess him and fire into the far corner past Dean Henderson. 1-0 Villa.
35th min: Fernandes attempts a spectacular long-range effort with Martinez off his line, but the playmaker's effort is far too high.
39th min: Rashford's side-footed effort from outside the area is straight down Martinez's throat, and the Argentine holds onto the ball once again.
45 +1 min: Ollie Watkins is presented with a chance to double Villa's lead just before the break, but his effort is too tame and Henderson gets down to save.
48th min: Pogba has plenty of time to set himself for a shot, but his effort deflects off Tyrone Mings and out for a corner, which comes to nothing.
50th min: Henderson gets down low to save from El Ghazi after a fast Villa break, but Ross Barkley was offside in the build-up anyway.
52nd min: United quickly restore parity. Douglas Luiz gives away another penalty against United after needlessly bringing down Pogba. Fernandes steps up and calmly sends Martinez the wrong way. 1-1.
56th min: Solskjaer's side get the second goal that their second half performance warrants. Aaron Wan-Bissaka finds a gap and picks out Greenwood, who expertly turns away from Mings before powering home a left-footed effort into the bottom corner. 1-2.
59th min: Fernandes picks out Harry Maguire at the back stick, but the centre-back's header is too high to trouble Martinez.
60th min: Traore so nearly bags his second of the game, with Henderson having to turn it away for a corner, which comes to nothing despite a handball appeal.
63rd min: Rashford's long-range effort takes a deflection on its way behind for a corner, but Villa survive.
76th min: Barkley fires a shot away following a free kick, but the ball sails over the bar as United seek to preserve their lead.
83rd min: Villa push for an equaliser and Traore gets another shot away, which is far too soft to beat Henderson in the middle of his goal.
87th min: Game set and match. Substitute Edinson Cavani once again shows his quality with some brilliant movement in the Villa box, and he meets Rashford's cross to direct a deft header into the bottom corner. 1-3.
89th min: Watkins goes down under a challenge from Henderson, but he is adjudged to have dived and is given his marching orders for a second yellow card.
MAN OF THE MATCH - LUKE SHAW
Despite not being able to increase his goal contributions for the season, Luke Shaw was a constant threat down the left-hand side for United, consistently giving Traore and Matty Cash a whole host of problems.
The left-back showed glimpses of a fruitful partnership developing with Pogba down that side, and today's performance reflected what has been his best-ever season in a United shirt.
Luiz was again the culprit, and Pogba was again the victim as Chris Kavanagh pointed to the penalty spot early in the second half, with Fernandes's spot kick representing the 113th penalty given this season - a new record in the Premier League.
In typical Fernandes fashion, the Portuguese playmaker gave Martinez the eyes before slotting home for his 25th Premier League goal - a tally achieved in just 48 matches in a United shirt.
Possession: Aston Villa 40%-60% Man United
Shots: Aston Villa 11-18 Man United
Shots on target: Aston Villa 5-7 Man United
Corners: Aston Villa 5-6 Man United
Fouls: Aston Villa 13-17 Man United
ASTON VILLA (4-2-3-1): Martinez; Cash, Konsa, Mings, Targett; Luiz (Ramsey 65'), McGinn; Traore, Barkley (Davis 78'), El Ghazi (Wesley 78'); Watkins
MANCHESTER UNITED (4-2-3-1): Henderson; Wan-Bissaka, Lindelof, Maguire (Bailly 78'), Shaw; Fred, McTominay; Greenwood (Cavani 65'), Fernandes (Matic 86'), Pogba; Rashford
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