Zoltan Gera gave Roy Hodgson’s side a fairytale start at Stamford Bridge when he struck after just four minutes and Fulham looked comfortable for the first hour.
But then Chelsea moved through the gears and were rewarded with two goals in two minutes (73 and 75) with Didier Drogba heading in an equaliser before the pressure forced defender Chris Smalling to concede an own goal.
It was a cruel blow for Fulham who defended heroically until the Blues’ onslaught began to take its toll.
Smalling, deputising for the injured Brede Hangeland, will feel particularly aggrieved after making a fine full debut – until he turned the ball into his own net.
Former Blues boss Jose Mourinho watched from the stands.