Marcus Rashford's first half strike kept United on course for a top four finish and condemned managerless Villa to the Championship.
The drop had looked inevitable for months but, in a match lacking tempo and intensity, this result rubber stamped their relegation.
After the Reds eye catching performance in midweek, a much changed side were not at their best but did enough to earn the three points and keep up the pressure on City.
Louis van Gaal made five changes from the side that won at West Ham in midweek and that- coupled with a second game in four games- no doubt played a part in a narrow win that was expected to be a rout.
Jordan Ayew skied the game's first attempt, Marcos Rojo headed over the top and Joleon Lescott sliced narrowly past his own post from Rashford's teasing delivery.
Juan Mata skewed wide having jinked into a good position and ex-Red Kieran Richardson fired over when Marouane Fellaini's header had dropped to him.
The brightest moment of the half arrived just beyond the half hour and led to the game's first-and only- goal.
The returning Wayne Rooney was fouled by Lescott in midfield and found the overlapping Antonio Valencia from the set-piece.
The right back's cross was missed by the stretching Villa defence and arrived in the middle for Rashford to supply a predatory finish past Brad Guzan for his seventh goal in 12 games.
United searched for a second to effectively end the game as a contest but Rashford was unable to profit when twice played through by Mata, firstly being hustled of his stride by Alan Hutton before he dragged his finish wide.
Memphis lashed off target and Guzan saved well from the lively Mata, but Villa grew into the game and went close through Scott Sinclair's header at the other end.
Villa suddenly sensed a goal as substitute Rudy Gestede hit a post from Ashley Westwood's corner and, from the resultant set-piece, Ciaran Clark forced a smart stop from the otherwise unemployed David de Gea.
Gestede was causing United problems and went close again with a header whilst substitute Anthony Martial linked up well with Memphis whom saw his effort turned on to a post by Guzan.
Not the easy victory that many predicted but all that matters now is the result and United were deserved winners as we kept alive hopes of a top four finish.
Villa, meanwhile, face life outside the top flight for the first time since 1987.
Overall team performance: 6/10
United Faithful Man of the Match: Marcus Rashford