Wilshere produced a composed display and was the heartbeat of the Arsenal side.
Wenger said: "Jack is getting closer to the player we know he is and today I think he made a big step.
"You could see it already this week in training, that he has gained a little burst again, a little zip in the first three or four yards.
"In football, you have sometimes to be patient. He can only gain it by playing but of course in the first games you cannot be at that level."