Christian Eriksen completed an unlikely comeback after we trailed 3-0 at The Hawthorns on Saturday.
West Brom blazed into a 2-0 lead inside four minutes, we then missed a penalty and when Stephane Sessegnon made it 3-0 on 31 minutes, it looked all over.
But Kyle Naughton's cross was deflected home for 3-1 minutes later, Harry Kane powered home Aaron Lennon's cross on 70 minutes and Eriksen pinged a shot into the top corner in the fourth minute of added time to secure a point.
The game kicked off at 3.07pm as a mark of respect to those who died at Hillsborough 25 years ago and a minute's silence was observed at the Hawthorns.
Less than 30 seconds were on the clock when West Brom snapped into action and seized the lead. A cross from Morgan Amalfitano was well diverted by Hugo Lloris but it was Vydra who was alert to the loose ball and smashed back into an unguarded net.
Just four minutes in it got worse when Vydra's cross was deflected upwards and fell kindly for Brunt to execute a fine volleyed finish.
Kane came fairly close to reducing the early deficit, shooting wide after a short run, before minutes later failing to find the target after reacting to a Danny Rose cross.
Emmanuel Adebayor had the chance to launch a comeback when Rose was adjudged to have been fouled by Amalfitano in the penalty area. The striker stroked the ball to the keeper's left and Ben Foster guessed right and foiled the spot kick with apparent ease.
West Brom would have made it three but for a stunning save by Lloris on 25 minutes to deny Amalfitano, but respite only lasted a further six minutes.
Younes Kaboul headed back towards goal leaving Vlad Chiriches in a direct race with Stephane Sessegnon, who won the chase and slotted powerfully past Lloris.
The deficit was quickly reduced when Kane picked out the run of Kyle Naughton. The full-back's delivery into the danger area looped up off the attempted interception of Jonas Olsson and flew over the despairing dive of Foster and into the net.
Zeki Fryers took over from Chiriches for the second half, the first chance of this period falling to Rose from a diverted Chadli cross, with the full-back hitting his shot across the face of the goal. With a bit of momentum, Aaron Lennon then forced a fine low save from Foster.
Foster was again called into action to parry away a Christian Eriksen free-kick that most thought would be simply flighted into the area. Rose was booked by referee Mr Swarbrick for falling under a challenge from Steven Reid that the West Brom player appeared to pull out of at the last second.
West Brom were wobbling a little as they were put under sustained pressure for the first time. Kane was unlucky on two occasions in not connecting with crosses from Naughton and Paulinho.
The home side's lead was cut to one in the 70th minute following a darting run and cross from Lennon that was met at the far post by the head of Kane, with the goalkeeper and defender getting into a muddle on the line and failing to prevent the header landing in the net. It was game on with interest.
Gylfi Sigurdsson took over from Chadli with 14 minutes left on the clock, but the next big chance fell to Rose after being set up by Adebayor, but the effort blazed over.
Rose was replaced by Andros Townsend for the closing stages and an all out assault on the home goal followed.
Our efforts were finally rewarded four minutes into six minutes added time when Lennon's cross fell to Eriksen and the Dane was coolness personified, switching onto his right foot before blasting into the top corner.
West Brom: Foster; Reid, McAuley, Olsson (Dawson, 77), Ridgewell; Amalfitano, Mulumbu, Brunt, Dorrans; Sessegnon (Yacob, 59); Vydra (Berahino, 72). Unused subs: Myhill, Anichebe, Jones, Bifouma.
Spurs: Lloris; Naughton, Chiriches (Fryers, 46), Kaboul, Rose (Townsend, 85); Lennon, Chadli (Sigurdsson, 78), Paulinho, Eriksen; Adebayor, Kane. Unused subs: Friedel, Veljkovic, Bentaleb, Winks.
Yellow cards: West Brom - Dorrans, Reid, Foster. Spurs - Rose., Eriksen.
Goals: West Brom - Vydra (30seconds), Brunt (4), Sessegnon (31). Spurs - Naughton (34), Kane (70), Eriksen (90+4).
Referee: Mr N Swarbrick.
Attendance: To follow...