The victory - courtesy of goals from Wilshere and Lukas Podolski - combined with Schalke's win over Olympiakos, means Wenger's men have advanced to the last 16 of the Champions League with a game to spare.
After a poor first half Wilshere scored his first goal since his comeback from injury, clipping neatly over the goalkeeper from Olivier Giroud's cushioned header.
And Wenger was full of praise for the central midfielder.
"He's getting strong physically. Tonight he got in the box - he's the complete midfielder you know," he said.
"I believe he can defend well, attack well and these kinds of matches will give him confidence."
Arsenal are second in the group behind Schalke, and they need to beat Olympiakos in Greece and hope Montpellier hold or beat the Germans to finish top.
Wenger said: "We will try to finish top of the group. You always feel a bit guilty if you don't do it. There are groups where you have Dortmund first, Real Madrid second - you don't really know what is the best.
"But overall statistically it is still better to finish top because you feel you've done your better if you finish top of the group.
"We will try to win at Olympiacos and Montpellier can beat Schalke at home. We will take a full-strength team.
"In this competition you just want to get to the next round and win the game. That's all you can do. Now of course we go into a cup (knock-out) competition which is a little bit different. We have some time and it's important we go into March with our best team available.
"I found Montpellier well organised, strong in their challenges and quite aggressive so for us it was a question of being patient, not making mistakes, using our experience and wait for a chances.
"The first half we had problems in the transitions to go from defence to attack and in the second half it was better.
"We moved the ball quicker, made more incisive runs and scored two goals."