Welbeck, recalled in place of injured Robin van Persie, struck twice in three minutes for United who moved up one spot to eighth, 10 points behind leaders Arsenal.
United had suffered successive home defeats by Everton and Newcastle United that followed away draws with Cardiff City and Tottenham Hotspur but outclassed the hosts and had the game safe when Tom Cleverley struck on 52 minutes.
Before kickoff Welbeck had scored as many goals for England - three - this season as he had for United but he was in the right place to make the breakthrough on 15 minutes, poking home the rebound after Adnan Januzaj headed against the foot of the left hand upright.
His first Premier League goal since his first day of the season double against Swansea was followed swiftly by a second when he linked up with the impressive Antonio Valencia, feeding the Ecuadorian and then sprinting into the box to get on the end of his return cross.
Welbeck was inches away from a hat-trick when he slid a shot past the far post from a tight angle and also went close after the break when his chip over a stranded Brad Guzan was just too high.
Cleverley said earlier this week that some of his performances had been 'average' this season, but wore a broad smile after running on to Wayne Rooney's pass to beat Guzan with a low shot at his near post.
"It was a good job from us. The players did well and the only thing I would criticise is that we didn't score more goals," United manager David Moyes told Sky Sports.
"We were a bit sloppy in the first five minutes but after that played really well."
United received another boost when Scotland international midfielder Darren Fletcher, battling a chronic bowel condition, came off the bench for his first match appearance since late December last year.
The cheers from United fans for Fletcher were part-drowned out by the boos from the home end that greeted former Villa forward Ashley Young.
Villa, who began brightly but carried little threat once they had fallen behind, have won just one of their last 36 Premier League games against United.
Nathan Dyer scored for Swansea City but suffered a suspected fractured right ankle in the 1-1 draw at Norwich City.
Dyer flicked past John Ruddy on 12 minutes but was carried off on a stretcher late in the first half after a challenge with Sebastien Bassong.
"We have to wait a couple of days for an X-ray and a scan, and we all cross our fingers to hope it is not that bad," said Swansea manager Michael Laudrup. "That will overshadow everything else. It is just a game of football."
Norwich earned a point thanks to Gary Hooper's spectacular volley in first-half stoppage time.
Tottenham host Liverpool in a later kickoff (1600). A victory for the visitors would lift them back up to second spot.
(Writing by Justin Palmer, editing by Alan Baldwin)
