Goals from Pedro and Ruben Loftus-Cheek at either end of the match were enough to see Chelsea past Fulham in a 2-0 win in the West London Derby.
Fulham's second half performance troubled Chelsea but were unable to avoid defeat against their local rivals on Claudio Ranieri's return to Stamford Bridge.
Chelsea climb above Tottenham after they lost at Arsenal, while Fulham remain rock bottom and without a clean sheet all season.
Maurizio Sarri was criticised for his use of N'Golo Kante after last week's defeat at Spurs, but it was his work high up the pitch that helped give Chelsea the lead. The midfielder robbed Jean Michael Seri of possession and played in Pedro, who finished calmly from close range after four minutes.
Calum Chambers had Fulham's best chance of the first half with a speculative effort from 20 yards, but it was pushed away by Kepa Arrizabalaga.
At the other end, Olivier Giroud was slipped through by Eden Hazard, but he took the ball too wide and Sergio Rico saved from a tight angle.
The France striker had another chance to double the lead after Chelsea won possession high up the pitch again, but was unable to get a touch on Mateo Kovacic's low cross.
Ranieri brought on Aboubakar Kamara for Ryan Sessegnon and Floyd Ayite for Stefan Johansen at halftime in an attempt to liven up his side's performance.
Fulham started to look more dangerous following their double substitution, and nearly forced Antonio Rudiger into conceding an own goal from Cyrus Christie's cross, before Chambers' header was saved from the following corner.
Chambers had another stinging effort denied by Arrizabalaga as Fulham continued to crank up the pressure.
Alvaro Morata had a great chance to seal the win for Chelsea after 73 minutes, but his rebound from Hazard's initial shot was wayward.
Ruben Loftus-Cheek came off the bench to make sure of the points after 83 minutes, as Chelsea returned to winning ways in the Premier League.