Both sides were reduced to 10 men as Kyle Naughton's first half dismissal for handball was followed in the second half by James Collins getting his marching orders for a second bookable offence.
After a fine late save by Hugo Lloris, Eric Dier capped a dream debut by rounding goalkeeper Adrian to roll home a precious winner in the third minute of stoppage time - giving new Head Coach Mauricio Pochettino all three points in his first competitive game in charge.
West Ham: Adrian; O'Brien (Demel, 62), Collins, Reid, Cresswell; Downing, Kouyate, Noble, Nolan, Vaz Te (Diame, 68); Cole (Valencia, 81). Subs (not used): Jaaskelainen, Zarata, Poyet, Burke.
Spurs: Lloris; Naughton, Dier, Kaboul (C), Rose; Bentaleb, Capoue; Lennon (Townsend, 61), Eriksen, Lamela (Holtby, 61); Adebayor (Kane, 83). Subs (not used): Friedel, Davies, Dawson, Soldado.
Goals: Spurs - Dier (90+3).
Yellow cards: West Ham - Collins, Kouyate.
Red cards: West Ham - Collins (second yellow). Spurs - Naughton.
Referee: Mr C Foy.