Albion had to settle for a 1-1 draw at Leeds United on Sunday after conceding a stoppage-time equaliser.
Danny Welbeck looked to have won it with his first half finish, but Pascal Struijk's header in the second minute of stoppage time ensured that both teams took home a point.
Albion will be frustrated, having had chances to add to Welbeck's goal. Leeds had some good spells in the second half but seemed to have run out of ideas and energy when the substitute nodded home.
Albion drop to tenth ahead of next Sunday's finale at the Amex against West Ham United.
Graham Potter named a rare unchanged team while Leeds made three from their midweek 3-0 defeat to Chelsea.
The atmosphere was spine-tingling from the off as the home fans looked to play their part in dragging Leeds out of the relegation zone, but their hopes of sucking the ball into the net probably hadn’t counted on their own skipper standing in the way.
Three minutes in Joe Gelhardt looked to have beaten Rob Sanchez at a corner to fire in from close range, but Liam Cooper got in the way of the effort on the line.
It was a slice of fortune for Albion so early on, but the hosts were counting their own lucky stars when Moises Caicedo fired straight into the arms of Illan Meslier from six yards out, before Solly March beat the offside trap, only to drag well wide of the target after being found impressively by the in-form Leandro Trossard.
Gelhardt hammered wide and Pascal Gross shot straight at Ilan Meslier at his near post in what was an engaging opening 20 minutes.
But the hosts were undone a minute later. Yves Bissouma pinched possession 25-yards from his own goal before bombing forward and splitting the Leeds defence open with razor-sharp accuracy, finding Welbeck. Diego Llorente slipped, Meslier was lobbed and Albion had the lead.
Alexis Mac Allister looped a header over on 30 minutes and Welbeck was spared his blushes for a tame effort when through on goal as the offside flag went up.
Jesse Marsch had Robin Koch to thank for keeping Albion’s lead to a single goal when the German’s well-timed challenge stopped Trossard getting a strike away and Alexis Mac Allister couldn’t turn it home on the follow up.
The hosts returned for the second half with the bit between their teeth and it was only an outstretched boot from Lewis Dunk that kept Rodrigo's flicked effort from bringing things level after 54 minutes.
Trossard curled an effort over from the edge of the box, but Leeds kept coming as again Sanchez came to Albion's rescue to palm away an excellent free-kick from Raphinha which was heading for the top corner before the Brazil international poked wide as he stretched to reach Rodrigo's low cross.
Sanchez was in inspired form as the game wore on, tipping away Klich's effort as United piled on the pressure, but Albion would not yield.
Adam Lallana was introduced to calm things down in central midfield with 15 minutes to play for his 250th Premier League appearance.
The game should have been put to bed with five minutes to go when Trossard found Welbeck at the back post, but the striker glanced wide.
It would prove to be a turning point as Leeds found their equaliser deep into six added minutes.
Gelhardt's cross found Struijk at the back stick to head in, sending the home crowd into hysterics as it kept their Premier League survival hopes alive.
Albion: Sanchez, Cucurella, Dunk, Bissouma, Mac Allister, Trossard (Lamptey 87), Gross, Welbeck, March (Webster 62), Caicedo (Lallana 74), Veltman.
Unused subs: Steele, Maupay, Alzate, Duffy, Offiah, Ferguson.