Football has been paying tribute to the late midfield maestro all weekend and that will continue at Stamford Bridge where Wilkins, who captained the Blues at 18, was much-loved.
How David Moyes' side were even in a position to salvage something from the game will give Antonio Conte sleepless nights, given his side's total control until that point. Cesar Azpilicueta had given Chelsea the lead in he first half, attacking a loose ball in the six yard box with the help of some bad defending on West Ham's part.
They are 10 points adrift of 4th place team, Tottenham Hotspur and just six games to the end of the season - meanwhile, they have a chance to win a title this season as they will be playing Southampton in the semifinal of this year's FA Cup later this month.
West Ham had the game's first decent chance on 13 minutes as Marko Arnautovic was picked out with a long pass but Gary Cahill did well to thwart the Austrian forward.
Willian forced Hart into a sharp save on 36 minutes after being played in by Hazard, but the hosts scored from the resulting corner.
Morata failed to test Hart with a towering header that soared over the target on 55 minutes, while Moses curled a left-footed shot narrowly wide of the left post 14 minutes later after Masuaku lost possession inside his box.
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In the 24 minute Alvaro Morata found the back of the net for Chelsea, but his goal was disallowed due to him being an off-sides position.
Willian then twice came close to giving his side the lead.
However, West Ham fought back when substitute Hernandez fired home an emphatic finish in the 72nd minute.
And the Mexican striker had a cheeky message for Blues fans after the game.
Conte's side threw everything forward in search of a victor, but found Hart in inspired form.
I can not score against one team, I keep scoring against Chelsea.