Ange Postecoglou's men made the perfect start as Brennan Johnson tapped home a fifth-minute opener from close range, but the Hammers quickly restores parity courtesy of an unorthodox finish from captain Kurt Zouma.
Both sides had their fair share of chances to net the all-important winner in the second half, but the spoils were eventually shared from an entertaining London derby.
The result for Spurs leaves them in fifth place in the Premier League table and two points behind fourth-placed Aston Villa, who travel to the Etihad Stadium to face champions Manchester City on Wednesday.
As for West Ham, David Moyes's men have extended their winless top-flight run to four matches and remain seventh in the table, three points behind Manchester United in sixth and one point above Newcastle United - who drew 1-1 at home to Everton in eighth spot.
Both sides made a lively start to proceedings, and after Jarrod Bowen directed a decent chance from close range well off target in the third minute, Spurs went up the other end to open the scoring just two minutes later.
Timo Werner breezed past Vladimir Coufal down the left channel after being sent through by James Maddison, and the German whipped a low cross towards the near post for Johnson to flick a first-time finish beyond Lukasz Fabianski.
West Ham responded well, though, and looked particularly threatening from set-pieces, with their equaliser on the 19-minute mark coming from an inviting corner from Bowen.
Hammers captain Zouma made an intelligent run from the back post into a central position inside the six yard box to meet Bowen's delivery, and as he towered above the Spurs backline, he somehow used his back to direct the ball into the far corner.
More to follow.