West Brom, fresh from downing Manchester United last weekend, had ample opportunity to extend their lead after Claudio Yacob headed home a Morgan Amalfitano cross in the 42nd minute. But it was Arsenal who ended the game in the hunt for the three points after Wilshere - looking to replace reports of late-night smoking with more positive headlines - scored with a deflected first-time shot from 20 yards.
"He is an honest lad and when he's wrong he knows it," said his manager, Arsene Wenger, whose side go top of the table by virtue of scoring more goals than Liverpool. "Today the players do not get away with anything - we got away with a bit more. But what is more interesting for England and for Arsenal is that he shows the right response on the pitch."
After a slow start, West Brom gradually took control of the midfield, Yacob and Youssuf Mulumbu proving an effective double act in the central area. Aaron Ramsey, so prolific this season, went close when his low shot through a packed box was well saved by Boaz Myhill but West Brom were enjoying much more of the ball.
Their pressure paid off three minutes from the break. Amalfitano's initial corner was cleared but when Mulumbu produced a sublime piece of control and fed the ball straight back to him, the Frenchman produced a killer cross. Yacob met it decisively with his head and the the hosts were in front.
The second half began explosively, with wonderful chances at both ends inside the first three minutes. West Brom went first, Berahino galloping forward and making 30 yards before looking for Nicolas Anelka at the far post. The pass seemed perfect but Anelka made a mess of his finish and got the ball trapped between his feet.
Moments later Arsenal advanced, with Olivier Giroud's lay-off finding Wilshere 10 yards out only for a wayward finish to spare West Brom. The pace barely slowed before Anelka went even closer. Liam Ridgewell took advantage of a yawning gap on Arsenal's right flank to play in the veteran, who moved towards goal and opened his body only to sidefoot wide of the far post.
They were level after 63 minutes, with Wilshere the scorer. Mesut Oezil and Giroud were the instigators, with the latter rolling the ball to substitute Tomas Rosicky on the edge of the box. His one-touch pass sat up for Wilshere, who did not hesitate in unleashing a left-footed shot from 20 yards. A deflection off Jonas Olsson turned a decent looking effort into an unstoppable one.
Arsenal were buoyed and probably should have taken the lead when a cute chip from Oezil presented Giroud with a delicious chance to volley from 10 yards. He snatched at the shot, though, leaving Oezil to shake his head. The striker's struggles continued when a rejuvenated Wilshere picked him out with a glorious ball over the top. This time a heavy first touch and a brave smothering save by Myhill denied him.
"It was a tough game for me," said Wilshere. "I am not used to playing on the wing, I'm still learning it, but I'm happy to do it for the team. I got a goal, which was nice - I've always said I want to score more goals."