A late goal from Mason Mount proved the difference as Chelsea battled to victory against 10-man Fulham.
Chelsea had the best of a goalless first half at Craven Cottage, with Mount smashing a shot off the bar, before a low strike by Hakim Ziyech was tipped wide by Alphonse Areola.
A minute before half-time, Fulham’s task got harder as Antonee Robinson was sent off for a reckless challenge on Cesar Azpilicueta.
After the break, Chelsea continued to press for an opener with substitute Tammy Abraham heading a great chance straight at Areola.
The deadlock was finally broken on 78 minutes, when Areola palmed a cross from Ben Chilwell out into the path of Mount, who steered the ball in.
Fulham stay 18th, with 12 points, after a first defeat in six matches, while a first win in four lifts Chelsea to seventh on 29 points.
Fulham: 20 Jan v Man Utd (H)
Chelsea: 19 Jan v Leicester (A)