The Reds deservedly led at the interval as Antonio Valencia headed home Ryan Giggs' excellent cross in first-half injury-time, but the Gunners rallied after the break and looked set to take a share of the spoils when Robin van Persie squeezed home a leveller with 19 minutes remaining.
United hit back, however, and re-took the lead when Valencia capped a storming individual run by setting up Welbeck to power home a finish and keep the champions right on Manchester City's coat-tails at the head of the table.
The day began in disappointing fashion for the Reds after the Blues' dramatic win over Tottenham, yet ended on a high despite the news that Rio Ferdinand was missing from the champions' ranks with a back injury. That blow was softened by the return of Phil Jones and Jonny Evans. Evans lined up alongside Chris Smalling in the centre of defence, while Jones came in at right-back and Rafael dropped to the Reds' bench.
Arsenal were able to welcome back Thomas Vermaelen from injury; bringing a welcome dose of steel to a Gunners backline keen to shore up after back-to-back defeats at Fulham and Swansea.
Manchester City's last-gasp victory over Tottenham ramped up the pressure on the champions ahead of kick-off, and it was the hosts who had the first sniff of goal when Alex Oxlade-Chamberlain pinched possession from Jones, but could only pull his cross into a cluster of United defenders.