Mason Mount, who was the standout player for Frank Lampard’s side, struck the winner in the 77th minute to give Chelsea all three points.
Fulham impressed in the first half, trading blows with the Blues before Antonee Robinson was shown a straight red card for a reckless challenge on Chelsea captain Cesar Azpilicueta.
Despite the sending off, Chelsea failed to truly create any big chances and were even lucky not to concede themselves when Edouard Mendy made an error before Mount struck.
The win leaves Chelsea in seventh – one point behind Tottenham – while Fulham are left four points adrift of Burnley in 17th despite their spirited performance.
Alphonse Areola – 8. The French goalkeeper made a fine save to deny Giroud the opener inside 10 minutes, and made an even better one to deny Rudiger’s header from a corner. Perhaps he should have done better before the goal.
Ola Aina – 7. The former-Chelsea man got forward well in possession, but he showcased his defensive capabilities at Craven Cottage as he kept Pulisic quiet.
Joachim Andersen – 7. The Fulham captain was solid and give as good as he got throughout the London derby.
Tosin Adarabioyo – 7. Adarabioyo defended well as Fulham held off Chelsea in the first half, and he made some crucial interventions in the second period.
Kenny Tete – 6. The Dutch wing-back got forward at will for Fulham, and defended well too. He was much quieter in the second half.
Harrison Reed – 6. He was willing to run and be available but didn’t particularly impress.
Andre-Frank Anguissa – 7. The powerful midfielder dominated the battle with Jorginho and troubled Chelsea players at will.
Antonee Robinson – 5. The American showed off his pace when he left Azpilicueta for dead after 15 minutes, but he was lucky that Mount hit the bar after a poor header clear. Sent off for an overzealous challenge on Azpilicueta.
Bobby De Cordova-Reid – 6. The tricky midfielder started brightly, but his influence waned as Fulham dropped off following the red card.
Ivan Cavaleiro – 4. He gave the ball away cheaply when Aina looked to get forward, and stumbled over the ball when in a dangerous position. The forward missed the best chance of the first half when he spooned a shot over the bar.
Ademola Lookman – 6. His dribbling was an issue for Chelsea in the first half, and he dropped deep intelligently to kickstart Fulham moves. Struggled in the second period.
Aboubakar Kamara – 6.
Edouard Mendy – 5. The summer signing had almost nothing to do, and then needlessly rushed out to cause havoc in his own area.
Cesar Azpilicueta – 6. The Spaniard would have been glad to see the back of Robinson after the wing back’s pace was causing issues, and the Chelsea captain was on the receiving end of the awful challenge.
Antonio Rudiger – 6. The German defender was almost an unlikely scorer but his header was spectacularly saved by Areola.
Thiago Silva – 6. Shanked a clearance out of play under no pressure to start the second half, but he made a crucial block to deny Cavaleiro after Mendy’s error.
Ben Chilwell – 7. The England international bombed forward down the left and was a nuisance for Fulham, although he blazed a tricky volley over the crossbar. Defended well after a shaky start.
Jorginho – 5. He came off second-best in the battle with Anguissa, but distributed effectively. Withdrawn for Abraham.
Mateo Kovacic – 6. The Croatian was anonymous in midfield, overshadowed by Mount and outclassed by Anguissa.
Mason Mount – 9. The England international was composed in midfield and dictated the tempo of the match while making key defensive contributions. He was unlucky to hit the crossbar but he took his goal excellently.
Hakim Ziyech – 6. He found space to fire a goal-bound shot but was denied by Areola. The Moroccan supplied a dangerous ball but Pulisic just couldn’t get on the end of it. Ultimately, the summer signing was kept too quiet.
Christian Pulisic – 6. The American struggled to get going in the first half as he was shackled by Fulham’s defence. He found more space in the second half, but didn’t dribble at defenders quite as much as Chelsea would have liked.
Olivier Giroud – 5. Snatched at a shot early to force a finger-tip save out of Areola, but that was as good as it got for the Frenchman.
Callum Hudson-Odoi – 6.