The Blues took the lead early on when Pedro slotted home from N’Golo Kante’s pass and they could have had more in the first half had Sergio Rico not twice denied Olivier Giroud.
Fulham threatened to find an equaliser in the second half as Chelsea struggled for fluency, but substitute Ruben Loftus-Cheek made the win safe when he fired past Rico after an intricate passing move with Eden Hazard and Pedro.
Defeat for Fulham means they stay bottom of the table, having claimed only one point from a possible 24 away from home this season.
Chelsea bounced back from defeat by Tottenham with an emphatic 4-0 Europa League win over PAOK Salonika on Thursday and they followed that up with another, albeit more laboured, victory against Fulham.
It took Pedro just four minutes to break the deadlock as he tucked away Chelsea’s 1,000th Premier League goal at Stamford Bridge and that set the tone for the first half.
The hosts dominated possession in the first half and they could have easily had a second on 24 minutes when Giroud, who netted a double in midweek, saw his low effort blocked by Rico.
And the Spain goalkeeper was there to foil the Frenchman again on the brink of half-time, as he saved Giroud’s sliding effort from Cesar Azpilicueta’s cross.
However, Sarri’s team were unable to play with the same fluidity in the second period and they did not seriously test Rico again until Marcos Alonso’s whipped free-kick was saved on the hour mark.
Second-half substitute Alvaro Morata then wasted an excellent opportunity after 73 minutes when he fired over with the goal gaping after Rico had parried Hazard’s low strike.
But fellow replacement Loftus-Cheek was on hand to net Chelsea’s second of the game, and his fifth in his past six games, with eight minutes remaining.
The Blues’ victory means they are now unbeaten at Stamford Bridge in 14 matches in all competitions, a run which stretches back to April.
