The Baggies were ahead after just 30 seconds when Matej Vydra found the net, before Chris Brunt swept in to make it 2-0 with only four minutes gone.
After Emmanuel Adebayor had a penalty saved by Ben Foster, Stephane Sessegnon raced away and extended the hosts' lead on 31 minutes.
We pulled one back when Kyle Naughton's delivery was diverted into his own net by Jonas Olsson three minutes later, while it was 3-2 on the 70 minute mark when Harry Kane headed home.
Christian Eriksen then smashed the ball into the top corner in the fourth minute of added time to secure a share of the spoils.
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.