West Ham shocked the visitors in the seventh minute when Antonio got in front of Nacer Chadli on the near edge of the six-yard box and headed home a Dimitri Payet corner.
Home captain Mark Noble brought a fine save from Hugo Lloris with a thunderous long-range strike that the Frenchman had to dive full-length to claw away.
Tottenham's best chance came on the hour when Harry Kane somehow missed his kick in front of goal after West Ham keeper Adrian saved a low 25-metre drive from Toby Alderweireld.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
Spurs, who needed a win to go top, were aiming for a seventh successive league victory for the first time in almost 50 years but lost their first league match since mid-January.
(Reporting by Ken Ferris; Editing by Ed Osmond)
