But the restart saw the traffic in the same direction - towards the West Ham goal, and Willian, should have doubled the lead, but he slide the ball just wide of Hart's goal.
There was still time for Stephens and Elneny to receive straight red cards within a few minutes of each other for raising their hands.
David Moyes' side came under pressure from the home side after falling behind to Cesar Aziplicueta's opener from point-blank range in the first half. The most worrying part is, it's not a surprise, we've seen this time and time again this season.
For West Ham, it was a valuable point in their fight to beat the drop, with a sizable advantage now over the bottom three. West Ham had tentatively begun building possession, pushing Chelsea back and, as tensions rose inside Stamford Bridge, they grabbed an equaliser with just their third touch in the Chelsea penalty area.
Chelsea were in control but when Alvaro Morata found the back of the net from Hazard's pass, the Spain striker's effort was ruled out for offside.
West Ham were also indebted to a fine display in goal from Hart, who produced several brilliant saves in arguably his best display for the club since joining on loan from Manchester City.
In the past, Javier Hernandez was the super-sub at United who seldom failed to hurt Chelsea, and the situation has not much changed since then, as the talented figure delivered Conte's men a lethal blow last night.
Earlier, Danny Welbeck inspired Arsenal to a sixth straight victory with two goals and an assist in a hot-tempered 3-2 home win over Southampton, to leave the Saints still rooted in the Premier League relegation zone.
A great last-ditch tackle from N'Golo Kante halted Anoutovic in his tracks as he raced down on goal as the visitors went for the jugular.