The England midfielder was not at his best during the clash at The Hawthorns but put that behind him to come up with a 63rd minute equaliser in a much-improved second half showing.
Wilshere, who made headlines after it was reported he had been smoking during the week, cancelled out Claudio Yacob's 42nd minute header to send the Gunners back to the top of the table and pleasing manager Wenger.
"He had trouble today to find the rhythm of the game," Wenger said on Sky Sports 1.
"But he has character as well. He doesn't give up, he continues to play his game and got a great goal.
"I believe he was fouled a few times, pushed over and didn't get the fouls he deserved."
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