The Frenchman took charge of his 811th Gunners league game, taking him past Alex Ferguson’s Premier League record of 810.
But his side were denied victory by Jay Rodriguez’s 89th-minute penalty, awarded for handball against Calum Chambers to the fury of Wenger and his players.
Arsenal had taken the lead six minutes earlier after a deflected Alexis Sanchez free-kick found its way into the West Brom net via a deflection off James McClean.
The Gunners had been frustrated for much of the game by a resolute Albion. Arsenal made the brighter start but might have found themselves trailing to the first chance of the game on six minutes.
A weaving run down the right flank by Matt Phillips ended with a cross for Rodriguez, who leapt highest but headed too close to Petr Cech and the Arsenal goalkeeper made a solid save, diving to his left.
Cech handed the Baggies another chance moments later when he spilled a high cross by Kieran Gibbs at the feet of Hal Robson-Kanu.
The Wales striker’s effort was blocked and Arsenal then snuffed out Jake Livermore’s effort to keep the move alive.
That sparked an Arsenal counter-attack as the Gunners worked the ball to the edge of the area, where Alexandre Lacazette hit a shot that deflected wide.
And on 16 minutes a neat pass by Sanchez found Alex Iwobi, who wriggled away from Jonny Evans and bent a shot just past the angle of post and crossbar.
West Brom continued to pass the ball neatly but the Gunners threatened on the break and a long-range effort by Granit Xhaka was saved comfortably by Ben Foster, who then turned another shot from distance from Iwobi behind for a corner.
– West Brom pressure –
The hosts began the second half on the front foot, with Rodriguez forcing Chambers into a desperate challenge.
The visitors had failed to fire early in the second half but West Brom needed Foster to keep them at bay on the hour mark.
The Albion goalkeeper made a smart, low save to keep out a shot from Lacazette, who had played a neat one-two with Iwobi before riding two challenges on the edge of the area.
And moments later Lacazette poked a shot just wide after Sanchez had picked him out with a neat pass.
Arsenal had increasingly run out of ideas and an ambitious, long-range shot from Iwobi that Foster held easily was a sure sign of the visitors’ frustration.
The hosts threatened when Livermore arrived at the near post to meet a cross by substitute McClean but his effort was blocked by Cech. And Cech was then forced to beat away a shot from distance by Rodriguez.
But with seven minutes remaining the Gunners claimed the lead when Sanchez won the decisive free-kick. He was tripped on the edge of the 18-yard box by a combination of Gareth Barry and Craig Dawson.
The Chilean let fly with an effort that struck McClean’s leg and defeated Foster.
But just minutes later Albion were level as Chambers was punished harshly for blocking a Kieran Gibbs cross with his arm and Rodriguez drilled the resulting penalty low past Cech.
Wenger lost his cool on the touchline and was subjected to a lengthy lecture from the referee.
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