Eric Black's side went into the match knowing that only a win would further delay the inevitability of relegation, but Marcus Rashford got the only goal of the game to condemn the visitors to Championship football next season.
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Villa had only won one of their last 40 league meetings against United and just one of their last 30 visits to Old Trafford, and sure enough they found themselves on the back foot early on as the hosts dominated possession in the opening exchanges.
Clear openings were tough to come by, though, and Juan Mata squandered the best of the opening half-hour when he sliced an effort out for a throw-in having skipped inside from the right flank.
Kieran Richardson sliced a half-volley over the crossbar shortly afterwards on a rare foray into the United half for Villa, but the breakthrough finally came for the hosts just past the half-hour mark.
The returning Wayne Rooney sent a long pass out to Antonio Valencia, whose low cross into the middle was turned in by Rashford as the youngster made it seven goals in 12 appearances since breaking into the first team.
A curling effort from Rooney drew a routine save from Brad Guzan just three minutes later, before Villa ended the half with their first real sight of goal when Jordan Ayew cut inside, only to see his shot blocked by Smalling.
The second half immediately fell into a similar pattern and United almost doubled their lead in the opening minutes when Rashford stayed on his feet after a rash challenge from Alan Hutton inside the penalty area before firing a low strike narrowly wide moments later.
Memphis Depay saw a curling effort fly over as the hosts continued to dominate possession, while shortly after the hour mark Villa fell asleep from a corner and needed Guzan to deny Mata from a tight angle.
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They pulled the same trick again 16 minutes later and once more Villa were caught out, but this time Mata could only flash the ball across the face of goal.
For the most part, though, United's passing was far too laboured to really trouble the Villa defence, and the hosts almost paid the price for that as the visitors provided a late flurry in their final minutes before relegation.
A subsequent corner was hooked towards goal by Gestede but, with David de Gea rooted to the spot, the ball thumped off the post, before another corner moments later saw Ciaran Clark's header kept out by the United stopper.
United weathered the late Villa storm, though, and could have even doubled their lead in stoppage time when Anthony Martial fed a pass through to Depay, who saw his low shot saved by Guzan and bounce up off the post on its way behind.
The final whistle confirmed relegation for Villa for the first time since 1987 as they lost their status as Premier League ever-presents, succumbing to a ninth straight defeat to move within two losses of the worst run in the club's history.
United, meanwhile, move to within one point of fourth-placed Manchester City as they look to push their local rivals to the end in the race for the final Champions League spot.