David Lopez stretched Albion’s unbeaten run to five games with a penalty in the sixth minute of stoppage time to secure a 1-1 draw at Blackburn.
The hosts looked to be heading to victory in a poor game courtesy of a spot-kick from Scotland striker Jordan Rhodes a minute before half-time.
But seconds before the end David was fouled by David Goodwillie and the Spaniard dispatched the penalty for his fourth goal of the season.
Tomasz Kuszczak, whose fumble cost Albion two points at Birmingham on Saturday, twice came to Albion’s rescue in the first half.
He made a fine save low down to push away Jason Lowe’s shot after the Blackburn midfielder burst into the penalty area, then he did well to keep out Morten Gamst Pedersen’s left-foot strike.
However, Kuszczak could do nothing to stop Rhodes’ penalty in the 44th minute after Adam El-Abd was penalised for a foul on Pedersen.
Poyet made a double change on 55 minutes, throwing on Will Buckley and Mackail-Smith but Albion still struggled to carve out chances.
It took them until the 76th minute to force home keeper Jake Kean into any sort of save, a comfortable take from third substitute Will Hoskins’ shot.
Instead Blackburn looked the more likely to increase their lead with Kuszczak making further saves from Colin Kazim-Richards and Rhodes.
However, a lifeline came thanks to Goodwillie’s ungainly challenge and David kept his nerve to grab a last-gasp equaliser.