Welbeck, a boyhood United fan and a product of the Old Trafford youth system, headed home Alex Oxlade-Chamberlain's 57th-minute cross shortly after Granit Xhaka's deflected strike put the hosts in front.
It was only the 26-year-old's second goal of another campaign blighted by injuries and, as when his goal helped to knock United out of the FA Cup two years ago, he snubbed the trend of only engaging in a muted celebration against old employers.
"I grew up there and it's a special place in my life, but once we get on that pitch it's just business at the end of the day," he told Sky Sports. "It's for the team.
"When you score you've got to be happy. It's only normal."
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Arsenal remain sixth, but can leapfrog fifth-placed United with victory at Southampton on Wednesday and have a further game in hand on third-placed Liverpool, who are seven points clear of them on 70.
"It was really important for us to get the victory with our position in the table," said Welbeck.
"We need to be further up there – it's something that we're all disappointed about.
"But to get the victory and to hopefully have a good end to the season, it's a good start."
Aaron Ramsey was named man of the match after an all-action display and the Wales midfielder is enjoying the extra attacking licence granted to him by the 3-4-3 formation boss Arsene Wenger has deployed to good effect over recent weeks.
"I felt good in the games that I've been playing in and getting into goalscoring positions," Ramsey told Sky Sports.
"Playing in that formation gives me a bit more freedom. It's a formation we're still working on but it showed today we can be effective using it.
"We're just delighted for ourselves and for the fans as well. They deserve that, to go home with a smile on their face."