Victory left the title-holders seven points below the Champions League positions in eighth place, but it was a timely win for manager David Moyes after a desperate run of four games without a victory.
Marc Albrighton worked United goalkeeper David de Gea twice in the early stages, but Welbeck put United in command.
Deputizing for the injured Robin van Persie, the England forward broke the deadlock in the 15th minute when he slammed home after Adnan Januzaj headed against the post from a Rafael da Silva cross.
Villa were unable to contain United’s right-sided players and three minutes later, the visitors scored another goal from that flank, with Antonio Valencia crossing for the sliding Welbeck to score.
Wayne Rooney — playing in his 500th club game — and Welbeck both came close to extending United’s lead before Cleverley added a third in the 52nd minute with a first-time finish from Rooney’s pass.
In the day’s other fixture, Swansea City drew 1-1 at Norwich City in a match that was overshadowed by visiting goalscorer Nathan Dyer being stretchered off with a suspected fractured ankle.
Gary Hooper earned Norwich a share of the spoils in first-half stoppage-time with a superb volley.
Additional reporting by staff writer