Maurizio Sarri's men were beaten 3-1 by Tottenham last time out in the league but, after easing to a 4-0 win over PAOK in the UEFA Europa League, did not to produce its best to resume normal service.
Pedro pounced on a poor passage of play from the visitors to open the scoring after just four minutes, and an excellent team goal finished off by Ruben Loftus-Cheek made the points safe late on.
Fulham had briefly threatened a leveller before that decisive blow, making it an unhappy return to Stamford Bridge for Claudio Ranieri, whose side remain bottom, while Chelsea at least momentarily move up to third.
It took a mere 220 seconds for Fulham's defensive woes to continue as sloppy play in midfield led to Chelsea's opener, their 1000th home goal in the Premier League.
Cyrus Christie's poor pass put Jean Michael Seri in trouble and he was dispossessed by N'Golo Kante.
The France midfielder played in Pedro down the right and the former Barcelona winger finished in style, cleverly evading Alfie Mawson before slotting into the bottom-left corner.
Sergio Rico was left relatively helpless but the Fulham goalkeeper was required to prevent Olivier Giroud from doubling Chelsea's lead, producing a fine stop to keep out his close-range effort after the ex-Arsenal striker latched on to Cesar Azpilicueta's right-wing cross.
Fulham started the second half in much more promising fashion and Seri almost atoned for his earlier error, delivering a fine corner from which Calum Chambers saw his near-post header brilliantly kept out by Kepa Arrizabalaga.
Chambers forced Kepa into a diving save as Fulham threatened what had previously looked an extremely unlikely equaliser.
A glorious chance to end any Fulham hope went begging as substitute Alvaro Morata lashed over from point-blank range after Rico turned Eden Hazard's deflected effort into his path.
However, Rico was helpless as Loftus-Cheek finally put the game to bed, playing a part in and emphatically finishing off a wonderful move involving Pedro and Hazard.