Thomas Tuchel's men came from behind as substitutes Ben Chilwell and Kai Havertz cancelled out Michail Antonio's opener in a dramatic second-half.
But moments after Havertz struck in the 88th minute, a sloppy header from Reece James appeared to gift a late equaliser to the Hammers.
Goalkeeper Edouard Mendy beat Jarrod Bowen to the loose ball but Maxwell Cornet was on hand to smash the ball into an open net.
However, after a lengthy VAR check, referee Andy Madley was advised to check the 50/50 between Mendy and Bowen.
And David Moyes was left utterly raging as the goal was controversially overturned.
While the decision to disallow West Ham's equaliser will dominate headlines, both Chilwell and Havertz proved their worth after Chelsea's record-breaking transfer window.
New defenders Marc Cucurella, Wesley Fofana and Kalidou Koulibaly were all left in a heap as the made a total mess of a West Ham corner for Antonio's opening goal.
And Chilwell, who has lost his place in the side, changed the game with a brilliant equaliser.
He then turned provider for Havertz, who dropped to the bench having failed to score in Chelsea's opening five games.
With deadline day signing Pierre-Emerick Aubameyang watching on from the stands, it was a timely strike.