The England striker punished Antonio Valencia's shocking back pass just past the hour in the FA Cup quarter-final at Old Trafford to seal a 2-1 win for the Gunners.
His reaction was a mixture of joy, relief and a release of any pent up feeling of injustice at being cast off by United boss Louis van Gaal last summer.
Welbeck began his Arsenal career in style and a hat-trick in a Champions League game against Galatasaray in October looked set to light the blue touchpaper.
But the goals have dried up, partly because of injuries, and his winner against United was only his fourth goal for the club since he destroyed the Turkish side.
Arsenal manager Arsene Wenger selected Welbeck ahead of Olivier Giroud for the trip to United and his faith was repaid as the 16 million pounds ($24.17 million) signing put Arsenal into the last four where they will face either Reading or Bradford City.
"We want all to do well when we play against our former club to show we are great players but it is not easy to deal with the mental aspect of it," Wenger said in a news conference.
"He focused just on his game and played football the way he wanted to. He has showed mental strength.
"He wants to win, he is a team player. He is intelligent. He is a great talent and has done extremely well for the national team as well. He has produced a great performance, defensively and offensively."
Arsenal had not beaten United in any competition since May 2011 and had suffered two FA Cup defeats against their fellow 11-times winners since beating Alex Ferguson's side on penalties in the 2005 final in Cardiff.
Playing at a tempo that United could not maintain as the game wore on, however, Arsenal were worthy winners.
"I am pleased above all with the performance and the mental aspect of our game," Wenger said. "It was above all positive."
"We were on the front foot from the start and close them down, play with a high pace and I felt that we did that well."
(Reporting by Martyn Herman; Editing by Peter Rutherford)
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