Albion came from behind to share the points in the Black Country derby and to maintain the bragging rights over their Staffordshire neighbours.
The visitors fortuitously took the lead on the stroke of half time when Kyle Bartley's attempted clearance cannoned off the foot of Fabio Silva and looped over Sam Johnstone.
But Albion were much improved after the break and Mbaye Diange headed an equaliser just after the hour mark.
The draw extended Albion's unbeaten run against Wolves at The Hawthorns to almost a quarter of a century.
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