Under-fire Tottenham coach Tim Sherwood saw his side fall 3-0 behind after 31 minutes, but the visitors battled back to claim a point as West Brom - who surrendered a two-goal lead to draw their previous home game against Cardiff City 3-3 - were dragged deeper into the top-flight relegation battle.
Both Sherwood and opposite number Pepe Mel are facing end-of-season talks over their futures and a point apiece would have done little to alleviate the pressure on them, with West Brom now just three points above the bottom three.
The visitors had to come from behind to beat Southampton and Sunderland in recent weeks and Christian Eriksen's stoppage-time strike rescued them on Saturday, but their hopes of a UEFA Champions League berth now appear remote.
Matej Vydra put the hosts in front after only 30 seconds and a shell-shocked Tottenham outfit were two goals down four minutes in, when Chris Brunt marked his return from injury by scoring a sweet left-foot volley.
Emmanuel Adebayor then had a poor penalty saved by Ben Foster and was made to pay when Stephane Sessegnon made it 3-0 to Mel's men.
But Jonas Olsson's own goal before half-time gave Tottenham hope and Harry Kane pulled another one back as the visitors dominated the second half, then Eriksen denied West Brom their first home win since New Year's Day three minutes into time added on.
Tottenham conceded after only two minutes in their last away game at Liverpool and made another slow start as the home side took the lead just 30 seconds in.
Morgan Amalfitano tormented Danny Rose down the right and whipped in a cross that Hugo Lloris could only palm into the path of Vydra, who fired home with his right foot.
Sherwood would have been hoping that setback would serve as a wake-up call to his side, but things went from bad to worse when the visitors fell two behind with just four minutes on the clock.
This time it was an unmarked Brunt who capitalised on some hesitant defending to volley home with his left foot at the back post after Sessegnon had headed a Steven Reid cross up in the air.
Tottenham were in disarray at the back, but Adebayor spurned a golden opportunity to reduce the deficit when his tame spot-kick was saved by Foster, diving to his left, after Amalfitano was adjudged to have fouled Rose 14 minutes in.
Lloris had to be alert to deny Amalfitano a third goal, but he was beaten again on the half-hour mark when Sessegnon outpaced Vlad Chiriches and kept his cool to slide the ball under the France goalkeeper.
Tottenham were then given a lifeline three minutes later, with Kyle Naughton's cross hitting the unfortunate Olsson and looping over Foster and into the far corner.
Foster produced a fine double save to deny Kane and Rose as the visitors looked increasingly dangerous going forward.
Tottenham went straight onto the front foot at the start of the second half and Foster produced a fine save to keep out Aaron Lennon's left-foot strike, then Rose felt Reid had upended him in the area but the left-back was booked for diving.
Kane raised hopes of a Tottenham comeback when he headed home Lennon's cross after 69 minutes to take his tally to two goals in as many Premier League starts for the club.
Sherwood cut a frustrated figure on the touchline as Tottenham threw everything at West Brom in the closing stages and the visitors were rewarded when the ball fell to Eriksen in the penalty area and he kept his composure to fire a right-foot strike beyond Foster.
With Fulham having beaten Norwich City, West Brom face a battle for survival in the closing five games.
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