Ashley Westwood's superb 13th-minute free-kick gave Villa hope of a rare Old Trafford victory but the outcome was ultimately all too familiar.
Wayne Rooney equalised with a 20th-minute header and put United ahead with a penalty on the stroke of half-time.
And after Christian Benteke had missed a glorious chance to level things up just after half-time, Juan Mata effectively put the issue beyond doubt with a third goal for the home side in the 57th minute.
Sub Javier Hernandez completed the scoring in stoppage time to inflict Villa's second consecutive 4-1 defeat.
Despite a plane hovering overhead with a banner calling for his departure, David Moyes was given a standing ovation by home supporters as he took the unusual step of making his way down the touchline before the teams emerged from the tunnel before kick-off.
If that was a bold statement of intent by the United manager, though, both sides started in tentative fashion, with chances in short supply at either end before Villa opened the scoring.
Benteke won possession before slipping a pass to Gabby Agbonlahor, who accelerated through the middle before being brought down by Rafael just outside the penalty area.
Westwood curled the free-kick right-footed over United's defensive wall, and although David De Gea made a despairing dive, the keeper could only help the ball into the corner of the net.
Ciaran Clark then ventured forward to head over from Marc Albrighton's free-kick before Brad Guzan was called into action for the first time.
It was a painful experience for the Villa keeper, who needed treatment after being caught by Rooney as he dived to collect Ashley Young's cross.
Guzan's nest task, unfortunately, was to collect the ball from the net after Rooney met Shinji Kagawa's delicate chip with a close-range glancing header which went in off the inside of a post.
Boosted by their equaliser, United threatened again a couple of minutes later, Clark blocking a Rooney shot just side the box before Ron Vlaar made a timely clearance to avert another menacing situation.
Although the game went flat for a while, Villa supporters were delighted when Vlaar displayed his creative flair following a 37th-minute corner which had been partially cleared.
The skipper turned past Marouane Fellaini on the left before delivering a fine cross which Rooney, of all people, cleared with a diving header.
Benteke had a shot charged down following another promising move.
But in the 45th minute, Villa found themselves behind, Rooney despatching his spot kick past Guzan after Leandro Bacuna had brought down Juan Mata as the Spaniard lined up a shot.
Four minutes after the break, the visitors should have been level, Westwood finding Benteke unmarked at the far post with a superbly measured centre.
The striker brought the ball under control but then miskicked completely, and as he lined up a second attempt sub Michael Carrick closed him down at the expense of a corner.
Benteke did considerably better a few minutes later, climbing above home skipper Nemanja Vidic to head just over from Albrighton's cross.
But in the 57th minute, United increased their lead when Mata fired home from eight yards after Fellaini's pass had fortuitously fallen into his path off Vlaar's heel.
As United continued to press, Guzan held a low shot from sub Adnan Januzaj and then produced an even better save to push away Rooney's drive.
Villa responded with a forceful run and shot over the bar from sub Aleksandar Tonev, who also curled a fine 84th-minute effort only narrowly wide.
In stoppage time, Hernandez added number four from close range following a Januzaj cross from the left.
Manchester United: De Gea; Rafael (Carrick HT), Vidic, Jones, Buttner; Young, Fellaini, Fletcher, Kagawa (Januzaj 68); Mata, Rooney (Hernandez 75). Unused subs: Amos, Giggs, Nani, Welbeck.
Villa: Guzan; Bacuna, Vlaar, Clark, Bertrand; Westwood, Delph; Albrighton (Lowton 78), Weimann, Agbonlahor (Tonev 71); Benteke. Unused subs: Steer, Bennett, Sylla Holt, Robinson.