After the Baggies raced into an early lead, Emmanuel Adebayor's penalty miss looked to have cost them badly but Harry Kane and Christian Eriksen at the death rescued a point
In an electrifying start, Matej Vydra opened the scoring within the first minute before Chris Brunt added a second just three minutes later to leave Tim Sherwood's side shellshocked.
The visitors had a chance to get back into it just after the quarter-hour when Danny Rose dubiously won a penalty but a dreadful effort by Emmanuel Adebayor was easily saved by Ben Foster.
Stephane Sessegnon made it three after roasting Vlad Chiriches but there was at hope for Spurs when Jonas Olsson put the ball into his own net shortly afterwards.
Harry Kane, making a rare start, got Tottenham back into it with a 70th-minute finish to Aaron Lennon's cross and then, right at the death, Christian Eriksen's shot was let go by a bunch of Baggies shirts to seal an unexpected point.
|VIEW FROM THE HAWTHORNS
|By Tom Davis
If West Brom learned how to close out leads, they would not find themselves in the troubled predicament in which they are currently are.
After pocketing such an impressive three-goal advantage here, they found themselves reflecting on dropped points yet again as they succumbed to a last-minute equaliser in a game much like the previous home tie, against Cardiff City, which also finished 3-3. Pepe Mel should have seen his side close this out but Christian Eriksen saved Spurs with his fourth goal in as many games.
Tottenham are all but out of the race for fourth place now and the Baggies are still in a relegation fight. As entertaining as it was, a point is not much good for either side.
Morgan Amalfitano tormented 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 penalty 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 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-footed strike, then Rose felt that Reid had upended him in the area but the left-back was booked for diving.
Kane raised hopes of a 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 Spurs 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 the playmaker 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.