Mason Mount finally broke the resistance of 10-man Fulham as Chelsea laboured their way to only a second Premier League win in seven games.
Antonee Robinson was sent off late in the first half for Fulham for a dangerous tackle on Cesar Azpilicueta.
Ten different players had shots for Chelsea, but they were wasteful in front of goal.
Their biggest chance before the goal was when Mount crashed a shot off the crossbar.
The England midfielder eventually proved the match-winner with a half-volley after Alphonse Areola flapped at Ben Chilwell’s cross.
The win takes Chelsea up to seventh, while Fulham – who had drawn their previous five league games – are four points from safety.