In the 18th score of the season to stroke, the corner of Giovani lo Celso and Harry Kane burst clear after that Czech midfielder Tomas Soucek accidentally converted to his own net.
The defeat still on goal gap for Bournemouth, Aston Villa and Norwich-who are in the bottom three-and each with a game in hand on the hands of David Moyes, puts the Hammers above the drop zone for the remaining seven fixtures.
Spurs felt they took the advantage on the half-time strike from Son Heung-min’s low shot, but the camera assistant referee adjudicated the South Korean to be slightly offside.
Kane flashed a shot over and dragged a large effort out of a swift counter-attack, though he might have scored earlier, while when it was 1-0 with 12 minutes left West Ham’s Jarrod Bowen rattled the post.
Tottenham – West Ham United 2:0
Goals: Souček 64 og, Kane 82.
Yellow Cards: Kane 51, Davies 67 – Fornals 15, Noble 26.