The Blues took the lead at Stamford Bridge through a first-half goal from Cesar Azpilicueta, only for Javier Hernandez to find a way through in the final quarter of the match to see the spoils shared.
There was a minute's applause before kick-off, with Chelsea's players all wearing number eight warm-up shirts in recognition of Wilkins' old jersey. But Hart was back in the team today, and put on a display he could be proud of.
In the 73 minute West Ham levelled matters when Marko Arnautovic slipped Chicharito through on goal and he made no mistake with just the keeper to beat, 1-1. His goal-bound effort was well blocked by Gary Cahill, making his first start since 10 March.
It was end to end action in the latter stages but Hart's resilience kept Chelsea at bay, thankfully our defence did just about enough to stop David Moyes' side from getting the victor.
Chelsea's persistent pressure eventually paid off thanks to Azpilicueta who prodded the ball home from close range after Morata headed back across goal from a corner.
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West Ham were nearly pegged back again on 79 minutes as Marcos Alonso fired a long range effort but Joe Hart produced a brilliant save to deny the Spanish defender.
Chelsea threw players forward in the final ten minutes of the game in search of a victor, but the London derby ended in a stalemate.
Chelsea will probably not qualify for the Champions League this season but with Manchester City having failed to win on Saturday, the Blues are still the reigning champions - for now at least.
Chelsea went into this game unbeaten in their last 11 home Premier League games against West Ham since a 2-3 defeat in 2002.
Joe Hart has claimed he is fully focused on helping West Ham avoid a relegation dogfight, rather than his chances of securing a spot in England's World Cup squad. David Moyes' squad has lost three out of its last four matches, but defeated Chelsea in December in will be looking to move further from the drop zone.