But once Welbeck rattled in the rebound after Adnan Januzaj had headed against a post, there was never much chance of it happening en-route to a 3-0 win.
Welbeck, since the opening day of the season had not scored a single goal in the league , added another from Antonio Valencia’s cross.
Cleverley, who like Welbeck has been singled out for criticism by many supporters for his part in United’s struggles this term, net his first goal in a year from Wayne Rooney’s lay-off.
It was lapped up by a vocal away support, who after the opener amusingly chanted: “We are staying up.”
Whilst presiding over a relegation battle in the season after replacing Sir Alex Ferguson is evidently not going to happen, for Moyes, he can only hope it is a victory that kick starts the season.
Not that he will meet many opponents like Villa, for whom striker Christian Benteke was a major disappointment.
As Everton and Newcastle both ended long waits for wins at Old Trafford in the past fortnight, nothing could be taken for granted.
However, Villa Park has long been one of United’s favourite grounds and in the Premier League they remained undefeated there since the famous ‘You’ll win nothing with kids day’ in 1995.
And, thanks to Moyes, he found Villa in the most accommodating of moods.
The visitors helped themselves with their speed and intensity, a sharp improvement on grim recent performances. Villa were unable to match them and left far too many open spaces for United shirts to flood into.
Valencia gave Antonio Luna a torrid time and with the Spanish defender unsettled, Rafael was able to surge to the by-line and send over a superb cross that was met perfectly by Januzaj.
The teenager’s header flashed past Brad Guzan, and when it came bouncing back off a post, Welbeck was racing in to apply a first-time finish to the rebound.
Within three minutes, the visitors had struck again.
This time Valencia provided the opportunity, with Welbeck sliding between defenders to touch home.
It was the perfect way for United to answer their critics, and Welbeck to silence a few of his.
The England striker revelled in the responsibility of leading the attacking line as Robin van Persie starts his month on the sidelines, with Wayne Rooney dropping so deep at times, he was almost assuming the Paul Scholes creative role.
Rooney did skim the outside of a post after Valencia had opted to pass rather than shoot after driving deep into the area.
Welbeck spurned a glorious chance to claim his first senior hat-trick from a very similar position after Valencia had once again proved too hot to handle.
It was an all-too-familiar story for Villa, for whom Benteke was a shadow of the player who terrorised defences throughout last season.
A confrontation between David de Gea and Gabriel Agbonlahor, making his 300th Villa appearance, at the start of the second period suggested the hosts had received a blasting from manager Paul Lambert.
But pretty soon, Rooney had powered forward and slipped a pass to Cleverley, who drove home his first Premier League goal in almost exactly a year.
Soon afterwards, the England midfielder was throwing himself in front of an Andreas Weimann shot as United attempted to preserve their healthy advantage, a sign in itself of the determination in the away ranks to right the wrongs of a dreadful few weeks.
The return of Darren Fletcher after almost 12 months out with, and virtually three years affected by a chronic bowel condition, merely added to the party atmosphere amongst the away support.
De Gea denied Karim El Ahmadi after Welbeck had floated a chip onto the roof of Guzan’s goal but by then, thousands of Villa fans had already started to head for the exits.