United were far too strong for lowly Villa, but their opening goal came from a dubious penalty that left the hosts fuming.
In the 27th minute, United midfielder Bruno Fernandes spun into Ezri Konsa before tumbling in the area despite little evidence of a foul by the Villa defender.
The penalty stood after a VAR review and Fernandes slotted home his eighth goal since joining from Sporting Lisbon in January.
United doubled their lead in first half stoppage-time when 18-year-old Mason Greenwood scored his fourth goal in three games with a fierce finish.
Paul Pogba got the third in the 58th minute, the France midfielder bagging his first goal of an injury-hit season with a low curler from 18 yards.
Ole Gunnar Solskjaer’s fifth placed side move to within one point of fourth placed Leicester in the race to qualify for the Champions League.
United, unbeaten in their last 17 games in all competitions, are the first team in Premier League history to win four consecutive matches by a margin of three or more goals.
Second bottom Villa are four points from safety and haven’t won in six games since the restart.
There was more VAR controversy at Dean Court, with Tottenham left in danger of missing out on European competition for the first time since the 2009-10 season.
Jose Mourinho’s side were off-key for long periods, but could feel hard done by after Josh King’s push on Harry Kane in the penalty area went unpushed despite a VAR review in the first half.
Just a week after Tottenham were the victims of a harsh VAR decision in their loss at Sheffield United, Mourinho felt they were the victims of another bad mistake by the replay official.
“The same referee who did the VAR decision against Sheffield United, Michael Oliver. Opinions matter, It’s not only mine. Everybody knows that’s a penalty and when I say everybody, I mean everybody,” Mourinho said.
“Normally at minute five we would be winning 1-0 against a team in trouble, I think the game would be completely different.
“The game had the most important moment. You know when, you know who. Like Sheffield, the man of the match was not one of the players.”
On course for their lowest points total since 2011, this has been a season to forget for Tottenham, who have yet to see any significant improvement since Mourinho replaced the sacked Mauricio Pochettino in November.
Just a year after reaching the Champions League final, they sit in ninth place in the Premier League, 10 points off the top four and far from certain to make next season’s Europa League.
“The performance was not good enough. There was a lack of sharpness in the attacking areas,” Mourinho said.
Third bottom Bournemouth thought they had won it in stoppage-time, but Callum Wilson’s overhead kick clearly hit King’s hand on its way past Hugo Lloris and their celebrations were curtailed by VAR.
Eddie Howe’s men, without a win in nine matches, are three points from safety with just four games left to avoid relegation.
At Goodison Park, Southampton held Everton to a 1-1 draw as Danny Ings boosted his bid for the Premier League’s Golden Boot.
Southampton’s James Ward-Prowse won a penalty in the 28th minute when he was tripped by Andre Gomes, but the midfielder blazed his spot-kick against the crossbar.
Three minutes after that blunder, Ings put Southampton ahead.
Stuart Armstrong miscued his shot into Ings’ path and the striker rounded Jordan Pickford to claim his 19th league goal of the season, three behind the top-flight’s current leading scorer Jamie Vardy.
Richarlison equalised for Everton in the 43rd minute, the Brazilian taking Lucas Digne’s superb long pass in his stride before guiding a clinical finish over Alex McCarthy for his 14th goal of the season.