The Mexican's effort, driven into the corner after Marko Arnautovic's fine cut-back, moves David Moyes' team six points clear of the relegation places.
Chelsea huffed and Chelsea puffed and missed a few more chances (and Kanté made a goal-saving tackle at the other end) and then it was the referee's whistle to bring another sad end to proceedings at Stamford Bridge.
Respects paid, Chelsea had to focus on finding a way to end a damaging run of one win from their previous four league matches.
Hart had to be at his very best to keep Chelsea at bay, with Willian, Eden Hazard and Alvaro Morata all running West Ham ragged at times, although it would be defender Cesar Azpilicueta who got the breakthrough prior to the interval.
The same pair combined moments later, but Morata was unable to direct his back-flick from the Belgian's cross into Hart's far corner from close range.
But West Ham substitute Chicharito needed only three minutes on the pitch to stop the Blues honouring their former skipper with a victory.
On the hour mark Morata had a goal disallowed for the second time, once again he was denied because he was in an off-sides position.
All those near-misses came back to haunt Chelsea in the 73rd minute.
Willian was inches away from doubling Chelsea's lead early in the second half after Hazard's clever back-heel gave the Brazilian space to shoot just wide.
I can not score against one team, I keep scoring against Chelsea.