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.
Nine different players had shots for Chelsea, but they struggled to create too many clear-cut opportunities.
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.
His team didn’t play well, but one moment of calm, considered quality from Callum Hudson-Odoi set off a chain of events that led to Mason Mount’s 78th-minute winner.
Scott Parker has a word with the referee, clearly considering Antonee Robinson’s first-half sending off to be harsh. Fulham dug in well in the second half, but couldn’t hold out. When the pain subsides, Parker should take a lot of positives from that performance. But Fulham remain in 18th spot, four behind Burnley. Chelsea meanwhile leapfrog Southampton and West Ham into seventh place on 29 points.
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