In-form Dutchman van Persie made it 30 goals for 2011, the second a sublime finish, after referee Phil Dowd had played a fine advantage following a foul by Russell Martin, to maintain Arsenal's resurgence.
Wenger said: "We missed early chances in the first 20 minutes and then we were 1-0 down.
"It made the game difficult against a very dynamic Norwich side, but with our backs to the wall, we responded well.
"Once we were ahead, we controlled the game and never were really in trouble.
"Overall it was a very positive win, and the team is growing from game to game."
Wenger was quick to praise his captain, adding on Sky Sports 2: "He is exceptional, but we all know within the club that he's an exceptional player.
"Sometimes, what was in the way was the fact he was injured. Since he plays, Robin shows just how good he is."