Arsenal's Mesut Ozil, centre, keeps the ball from West Bromwich Albion's Billy Jones, right, and Morgan Amalfitano during their English Premier League soccer match at The Hawthorns Stadium, West Bromwich, England, Sunday Oct. 6, 2013. (Photo: AP)
The hosts had taken the lead shortly before half-time courtesy of Claudio Yacob and saw ex-Arsenal striker Nicolas Anelka spurn two good opportunities to double their advantage before Wilshere equalised with a deflected shot.
The goal represented a positive end to a week in which Wilshere had been pictured with a cigarette in his mouth on a night out, for which he was rebuked by manager Arsene Wenger.
It was also enough to lift Arsenal back to the summit by virtue of having scored more goals than Liverpool.
Although the result brought to an end the Gunners' 10-game winning streak, manager Wenger will be satisfied with a point after a searching examination at The Hawthorns.
West Brom had defeated Manchester United only last weekend and the draw represented the first points the Gunners have dropped since their defeat at home to Aston Villa on the season's opening day.
West Brom, meanwhile, can take heart from an excellent fortnight in which they have turned around what was a disappointing start by taking seven points from three games.
West Brom's anchoring midfield pairing of Youssouf Mulumbu and Yacob succeeded in denying the Gunners' creative trio of Mesut Ozil, Aaron Ramsey and Wilshere the chance to settle into their rhythm.
The visitors were largely restricted to efforts from long range, with their first presentable opportunity arriving in the 13th minute when Ramsey drove a 25-yard free-kick over the crossbar.
It was, in fact, Wojciech Szczesny who was the first goalkeeper extended when, two minutes later, Saido Berahino's strike took a wicked deflection off Mathieu Flamini, forcing the Arsenal custodian into a fine fingertip save.
Wenger's team had to work to create openings and on the rare occasions they did, they were guilty of profligacy, with Kieran Gibbs and Wilshere both shooting off target.
The significance of those misses became apparent three minutes before half-time when Albion concluded a period of dominance with the opening goal.
Arsenal could only clear their lines five yards outside the area to Mulumbu, who controlled and turned in one swift movement before feeding Morgan Amalfitano, wide on the right, and his pinpoint cross to the near post was converted by Yacob with a forceful downward header.
After a prolific pre-season, Anelka is yet to score for the Baggies in competitive action and there were further signs of ring-rust shortly after the restart.
Unmarked at the back post, he failed to control a cross from Berahino, making his first Premier League start after scoring the winner at Old Trafford last weekend, following a swift counter-attack.
The visitors had a chance of their own seconds later when Wilshere surged through, only to blaze over the crossbar.
It was a fine chance, yet the one that soon followed for Anelka was even better.
Liam Ridgewell showed presence of mind to slot an early ball down the left touchline, leaving Anelka clean through on goal from wide on the left.
With the angle tight, the Frenchman attempted a low curling effort into the far corner, but it crept agonisingly wide.
It proved a key moment, as by the 63rd minute the Gunners were level.
Giroud found substitute Tomas Rosicky on the edge of the area and he teed up Wilshere, whose powerful strike from 25 yards deflected off Jonas Olsson, leaving Albion goalkeeper Boaz Myhill wrong-footed.
Both sides went in search of a winner, but their efforts proved in vain.
Szczesny thwarted Billy Jones's fierce strike, while Myhill pulled off a superb smothering stop to deny Giroud from close range after Wilshere had released the Frenchman.
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