In a tight first half, Chelsea created more opportunities but West Ham made life difficult for the title contenders by offering their creative players very little freedom.
West Ham's goalkeeper was called into action just before the break to deny John Terry, who had lost his marker but failed to find the net with a header.
The Hammers missed a good opportunity to take the lead early in the second half when Stewart Downing curled a cross into the path of Andy Carroll but the striker missed the ball completely in the box to the relief of the Chelsea defence.
Hazard was inches away from finding the opening goal in the 67th minute but his drilled effort drifted just wide of Adrian's post.
The visitors dropped deeper to defend late on but they continued to make crucial blocks to frustrate the home supporters and Jose Mourinho.
West Ham were forced to desperately hang on for a draw in the closing stages as both Hazard and Frank Lampard came close to scoring a dramatic winner for the hosts in stoppage time before the referee blew the final whistle.