The attacking midfielder had been heavily criticised by manager Arsene Wenger after newspaper images emerged of him smoking a cigarette outside a nightclub earlier in the week, but was quick on the draw as he saw a shot come off the boot of Jonas Olsson before speeding past home goalkeeper Boaz Myhill on 63 minutes.
It was Wilshere's first league goal since a 4-2 win at Aston Villa in November 2010. He had played 54 Premier League matches since his last goal.
A draw ends Arsenal's record run of eight successive away wins in the Premier League, but they did not do enough to claim all three points with West Brom producing a stout performance in front of their fans.
Wenger has the consolation of seeing his side return to the top of the standings on goals scored ahead of Liverpool. Arsenal have 16 points from seven games.
38' - RAMSEY EFFORT: Ozil's corner comes out to Ramsey, whose shot from distance is brilliantly parried clear by the diving Myhill. Superb stop from him.
42' - YACOB HEADER: Yacob arrives to head into the net from the Morgan Amalfitano cross. Brilliant delivery and finish. West Brom lead 1-0.
47' - ANELKA MISS: Glorious chance for Anelka to add a second for the home side, but he can't convert in front of goal. Should have been a second for West Brom.
48' - WILSHERE PENALTY CLAIM: Wilshere denied a clear penalty. Wallops the shot over, but clearly taken out of the action late by Jones. Bad decision by the referee. Or non-decision.
52' - ANOTHER ANELKA MISS: Anelka misses a glorious chance to add the second. Through on goal, but he knocks the ball inches wide.
63' - WILSHERE STRIKES: Rosicky picks out Wilshere and he thumps the ball into the net from 25 yards. Deflects off Olsson. Arsenal are level at 1-1.
76' - MULUMBU TACKLE: Youssuf Mulumbu makes a brilliant tackle on Wilshere as he was about to pull the trigger. Appeals for a penalty, but that was a fantastic challenge.
TALKING POINT: Was this a positive result for Arsenal? They might not have picked up three points, but Arsenal fans will probably be happy enough with a point. West Brom did a fine job in strangling the midfield. Arsenal improved after half-time, and Wilshere's effort helped them get out of town with their unbeaten away record intact.
Arsenal are now unbeaten in 18 Premier League matches following a European tie (W13-D5). It is the 16th consecutive Premier League away match they have scored, their best run in the Premier League since netting in 27 away matches in a row between May 2001 and December 2002.
Arsenal fail to set a new club record of nine top flight away wins in a row. West Brom end a run of four straight Premier League defeats against Arsenal.
Jack Wilshere is the first English player to score for Arsenal against West Brom in the Premier League since Francis Jeffers scored in a 2-1 away win in December 2002.
Nicolas Anelka has scored one goal in his last 25 Premier League matches. That was scored for Chelsea against West Brom in a 2-1 home win in August 2011.
West Brom: Myhill 8, Jones 7, McAuley 7, Olsson 7, Ridgewell 7; Yacob 7, Mulumbu 8, Amalfitano 7, Sessegnon 6; Berahino 6, Anelka 5. Subs: Morrison 6, Brunt 6, Long 5.
Arsenal: Szczesny 7, Jenkinson 7, Koscielny 6, Mertesacker 6, Gibbs 7, Arteta 6, Flamini 6, Ramsey 7, Wilshere 8, Ozil 6, Giroud 6. Subs: Rosicky 7, Bendtner 7.
MAN OF THE MATCH
Youssuf Mulumbu (West Brom): An industrious performance at the heart of the West Brom midfield. Produced one tackle on Jack Wilshere that had to be timed perfectly in the penalty area.
THE MATCH IN A TWEET