New signing Brandon Thomas-Asante came off the bench to snatch a draw for Albion on his debut as Albion drew 1-1 with high-flying Burnley.
The Baggies looked threatening going forward and saw efforts from Jed Wallace and Conor Townsend go wide before Kyle Bartley headed across the bar.
But the visitors took the lead against the run of play when Nathan Tella was fouled in the area by David Button. Old boy Jay Rodriguez stepped up to slot home the resulting penalty.
Albion looked to be heading for their first defeat of the season at The Hawthorns befroe Thomas-Asante's introduction.
The new signing from Salford smartly converted Conor Townsend's cross in the 96th minute as the home crowd errupted with the late goal.