Welbeck netted his first career hat-trick as the Premier League side ran out dominant 4-1 winners over Galatasaray in UEFA Champions League Group D.
In Arsenal's opening 2-0 defeat at Borussia Dortmund, deadline day signing Welbeck was guilty of missing a pair of clear chances, but he more than made amends as the impressive Alexis Sanchez also got his name on the scoresheet.
Alexis blotted his copybook by giving away possession in the move that saw Arsenal goalkeeper Wojciech Szczesny sent off for a professional foul on Burak Yilmaz, who converted the 63rd-minute penalty.
But there remained plenty of positives for Wenger to focus upon, not least Welbeck's stellar display.
"He had a great performance," Wenger told Sky Sports. "He added that instinct of a goalscorer, was more aggressive and made great runs.
"He finished the work of the team well. Overall the team played well until we were down to 10 men - then you could see how quickly you can lose control of a game. But the overall performance was still great.
"He has such good pace that it gives him time to finish calmly. Once a player understands that their finishing soon improves a lot."
Alexis was central to the pace and directness that tore Galatasaray apart and Wenger praised the former Barcelona attacker's best performance in an Arsenal shirt despite his later error - a final contribution before making way for substitute goalkeeper David Ospina.
"He played well, made some good passes apart from the goal we conceded," Wenger said.
"But before that I thought he had a very good performance."
Wenger refused to criticise Szczesny - the Poland international having also received his marching orders in last season's second-round defeat to Bayern Munich at the Emirates Stadium - but saw the incident as a lesson for his team to guard against complacency.
"It's difficult for him," Wenger added. "It's a fraction of a second. He has to come out and makes a penalty.
"When you lose the ball in your own half like we did those kind of things can happen.
"That's the problem in the Champions League - the opponent never gives up and you can only keep consistent domination of the game if you keep your concentration.
"We just relaxed a little bit with the fourth goal."
Welbeck was just five years old when Wenger took over in north London and the former Manchester United player was glowing in his praise of his new manager.
"He's shown a lot of faith in me and I'm delighted to be paying him back," he said.
"Giving me a chance to play up front in my preferred position, I'm going to do everything I can to make sure that he's happy."
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