Former Chelsea player Emerson Palmieri scored against his former club to earn West Ham a point and increase the pressure on Blues boss Graham Potter.
Chelsea fielded a new-look £200m forward line but, despite taking the lead, were once again frustrated and have won just once in seven Premier League matches.
Joao Felix had already had a goal ruled out for offside when the Portugal forward fired visitors Chelsea ahead with a volleyed finish following a delicious assist by Enzo Fernandez, the £107m British transfer-record signing from Benfica.
Kai Havertz thought he had doubled the lead only for Chelsea's celebrations to be cut short by another offside flag, before West Ham equalised through Italy international Emerson's first Premier League goal.