Maurizio Sarri's side, rejuvenated by a cathartic victory over Tottenham in midweek, took the lead after 20 minutes as Gonzalo Higuain diverted Cesar Azpilicueta's low cross past Sergio Rico.
Yet, just seven minutes later, Chelsea were caught out by Arsenal loanee Calum Chambers, who dropped into space at the back post and rifled home from the corner.
Moments later, though, Chelsea were back in front after the impressive Jorginho lingered on the edge of the box for Eden Hazard's lay-off and delivered a fine whipped finish into the top corner from 18 yards.
Kepa Arrizabalaga, reinstated as Sarri's first-choice goalkeeper after the Carabao Cup debacle, made a number of fine saves to keep Fulham at bay in the second-half as Sarri's side utlimately held on for the vital three points.
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