Manuel Lanzini's scrappy 65th-minute effort decided a derby that Tottenham had largely dominated without ever reaching the levels that had raised hopes of a first title since 1961.
Tottenham could have cut leaders' Chelsea's advantage to one point with a victory but instead the gap will stretch to a seemingly unbridgeable seven with three games left if Chelsea beat struggling Middlesbrough at home on Monday.
West Ham, the first team to stop Tottenham scoring since Liverpool in early February, moved up to ninth with 42 points and are now mathematically safe.
Home keeper Adrian frustrated Tottenham with first-half saves in quick succession from Dele Alli and Harry Kane and he also did well to keep out Son Heung-Min after the break as the visitors probed for an opener.
Tottenham were stunned though when West Ham broke forward and Aaron Cresswell's cross eventually squirmed its way to Lanzini who smashed the ball past Hugo Lloris from six metres out to speak wild celebrations around the ground.
Chelsea now need six points from their last four games to be crowned champions in Antonio Conte's first season in charge.
(Reporting by Martyn Herman, editing by Pritha Sarkar)
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