Villa had started the match brightly, but the roof caved in on their aspirations when Welbeck scored twice on 15 and 18 minutes.
The England forward pounced for his first on the rebound after Adnan Januzaj saw a header from a Rafael cross come back off a post before slotting Antonio Valencia's cross for the second.
Tom Cleverly finished off a Wayne Rooney pass on 52 minutes after Villa had needlessly shed possession.
The United fans could relax and were treated to the sight of Scotland midfielder Fletcher - missing due to ongoing treatment of the serious stomach condition, ulcerative colitis - playing his first match since Boxing Day when he replaced Ryan Giggs with 20 minutes remaining.
United remain eighth in the standings, 10 points behind leaders Arsenal, but they can be content with their afternoon's work at Villa Park.
15' - WELBECK STRIKES: Welbeck scores for United. Rafael with the cross for Adnan Januzaj. His header comes back off a post, but Welbeck follows up on to score with the volley. A 1-0 lead for United.
18' - WELBECK ADDS A SECOND GOAL: Welbeck scores a second goal for United. Villa shedding possesion needlessly. Valencia with the cross. Fine goal. A 2-0 lead for the visitors.
26' - VALENCIA THREAT: Glorious chance for Valencia to add the third, but he goes for the cutback when a shot at goal would have been better. Villa clear.
27' - ROONEY SO CLOSE: Valencia again involved to nudge Luna off the ball. Plays provider for Rooney, but his England companion drives a loose ball inches wide.
32' - UNITED DOMINANCE CONTINUES: Another chance for Welbeck. Give Baker the slip on the run, but he screws a shot inches wide of the home goal. So near yet so far for Welbeck.
52' - CLEVERLEY CLINCHER: Cleverley runs onto the pass from Rooney to slide the ball beyond Guzan. A 3-0 lead for United. That surely is that.
84' - WELBECK AWARENESS: Terrific backhees by Welbeck to play in Cleverley. Plenty of power on the shot, but swiped over the bar by De Gea in the visiting goal.
Man United end a four-match winless streak which takes them to 25 points this season. It's 14 points less than they had at this point last season, and remains their worst start in over a decade, since 2000/01, when they had 24 points after 16 matches.
Darren Fletcher, replacing Ryan Giggs, makes his first Premier League appearance since 26 December 2012, when he played in a 4-3 win over Newcastle United. He made only 11 appearances in the league over the past two seasons.
Tom Cleverley scores his sixth Premier League goal exactly one year after scoring his 5th in a 3-1 win over Sunderland on 15 Dec 2012.
Danny Welbeck scored his second brace of the season, and only the third Premier League brace in his career. He has never scored a PL hat-trick in 100 appearances.
TALKING POINT: Is Christian Benteke a one-season wonder? Benteke has now gone over 11 hours without scoring a goal for Villa. Changed days from last season when he plundered 28 goals from 50 appearances for club and country. Benteke last scored on September 14 against Newcastle. Too early to say if he is in a Fernando Torres-style depression, but he remains his club's top goalscorer with five goals. Which says enough about Villa's shortcomings in the forward areas.
MAN OF THE MATCH
Danny Welbeck (Manchester United): Came up with two fine goals to knock the stuffing out of Villa. Some fine movement and awareness.
Aston Villa: Guzan 6, Lowton 5, Clark 5, Baker 5, Luna 4, Westwood 5, El Ahmadi 5, Sylla 5, Albrighton 7, Agbonlahor 6, Benteke 4..subs: Weimann 6, Kozak 6, Bacuna 6
Manchester United: De Gea 7, Rafael 7, Jones 7, Evans 7, Evra 7, Valencia 7, Cleverley 7, Giggs 7, Januzaj 7, Rooney 8, Welbeck 8.subs: Young 6, Fletcher 6, Zaha 6