Premier League - United dig deep to win at Arsenal
Welbeck slammed the ball home 10 minutes from time after an excellent Valencia run, and the match ended amid discontent from the home crowd with manager Arsene Wenger's decision to replace the excellent Alex Oxlade-Chamberlain with Andrei Arshavin.
Though the Gunners did not suffer the humiliation of last autumn's 8-2 defeat at Old Trafford, they can take few positives from a muted performance.
United did not excel, particularly in the second half when they let their lead slip, but they had enough to overcome an ordinary Arsenal side.
Sir Alex Ferguson's back four again took on a makeshift look, with Rio Ferdinand missing out through injury.
Things got worse when Jones rolled his ankle and was stretchered off, with Rafael replacing him.
Nani was both United's brightest spark and their most wasteful player in a quiet first half.
His performance was summed up by a superb dribble inside from the left, leaving Djourou on his backside, but inexplicably chose to shoot from an impossible angle instead of looking for a team-mate.
When the breakthrough finally came, it was no surprise to see it come from the United left.
Nani made a simple pass to the overlapping Giggs, Djourou failed to close him down and the Welshman's cross was converted by a fine Valencia header. Djourou was replaced at half-time.
As a 38-year-old shone at one end of the pitch, Arsenal's best player was a man less than half his age - Oxlade-Chamberlain, making his first Premier League start.
The winger showed pace, skill and intelligence on the Arsenal left, far outshining the man to whom he is often compared, Theo Walcott.
Van Persie has been directly involved in over 60 per cent of Arsenal's goals this season, and his contribution would always be crucial.
But the Dutchman was guilty of an amazing miss on 51 minutes, firing wide with the goal gaping after Tomas Rosicky teed him up.
Nonetheless, Arsenal dominated as United inexplicably took their foot off the pedal, and it was no surprise when Van Persie levelled in the 71st minute.
Laurent Koscielny started the move with a superb tackle and quick pass, and Oxlade-Chamberlain set the striker up with a beautifully-weighted reverse pass.
Van Persie's finish was a belter, going through Evans's legs and bouncing in off the far post after Anders Lindegaard could get no more than a slight touch on it.
Wenger was preparing to take the teenager off when the goal went in, and pressed on with the change to a chorus of boos and open dissent from Van Persie.
And the anger doubled when Valencia breezed past Arshavin on his way into the box, where he teed up Welbeck for the winning goal.