West Brom, having shocked champions Manchester United last week, went for Arsenal despite their formidable away record, and came close to writing another headline-making victory.
Claudio Yacob, with his first goal for West Brom, headed them in front after 42 minutes and the Gunners, slow to settle and find their form, had to cling to the ropes for a while before fighting back.
Wilshere had been lambasted all week after being pictured smoking and looked as if he had been caught behind the school bike sheds by a teacher, not at the centre of things at all.
He was looking to make an impact but was mostly caught at the, er, fag end of what Arsenal were trying to do.
But in the second half, as Arsenal improved, so did Wilshere. Although a club-record ninth successive away league win wasn't on the cards for the Gunners, they deserved the draw.
Arsenal old boy Nicolas Anelka twice had chances to secure another famous win for West Brom early in the second half, before Wilshere snubbed out the threat with his first Premier League goal in three years.
Anelka, a key player in Arsenal's double year of 1997-98, lost the ball and a very good chance when he was set up by Saido Berahino.
He did better 10 minutes later when Liam Ridgewell sent him clear, but Anelka's cross-shot from the left still bounced a foot wide of the far post.
It was wastefulness that cost West Brom, because by the 64th minute their lead had gone.
Olivier Giroud, who by-passed two Albion players and then second-half sub Tomas Rosicky with his pass, set up Wilshere perfectly and he hit a 20-yard drive that had the huge help of a deflection off Albion's
Jonas Olsson to beat Boaz Myhill.
Wilshere's other Arsenal Premier League goal came just up the road at Aston Villa in a 4-2 win in November 2010, so in the West Midlands at least he's renowned for doing damage. But two goals in 62 league games is an amazingly lightweight return.
"Wilshere had a difficult first half where he was fouled a lot," said Wenger.
"He has shown his character and kept going. I don't think he was fouled dirty, but pushed over a lot. It's good that he was rewarded.
"I have not spoken to him about the smoking. He is an honest guy and when he's wrong he knows he is wrong. I don't know if he has stopped smoking.
"Today, the players don't get away with anything. We got away with more, but they know that is part of the game now, they have to deal with it.