Cheikhou Kouyate headed the Hammers into a first half lead, with Diafra Sakho rifling home from a tight angle to double his side's advantage shortly after the hour mark.
Danny Rose pulled a goal back on 81 minutes, his shot into the ground from 25 yards bouncing inside the far post, before Harry Kane was brought down by Alex Song in the fifth of five minutes of stoppage time and we were awarded a penalty.
Kane's spot kick was saved by Adrian, but the striker instinctively followed in - firing into the net to salvage a point with the last kick of the game.
Spurs: Lloris, Walker, Vertonghen, Dier, Rose, Mason (Chadli 80), Bentaleb, Townsend (Soldado 60), Dembele (Eriksen 45), Lamela, Kane. Substitutes (not used): Vorm, Davies, Fazio, Stambouli.
West Ham: Adrian, Jenkinson, Reid, Tomkins, Cresswell, Song, Kouyate, Noble (Cole 68, (Collins 87)), Downing, Sakho, Valencia (Jarvis 75). Substitutes (not used): Jaaskelainen, O’Brien, Demel, Nolan.
Goals: Spurs – Rose 81, Kane 90+6; West Ham – Kouyate 22, Sakho 62.
Yellow cards: West Ham – Noble, Cresswell.
Referee: Jon Moss.