The victory meant Enzo Maresca’s side have now lost just one of their last 12 league matches, underlining their strong early-season form.
The first half saw the visitors frustrate Chelsea, with Joao Pedro and Liam Delap threatening early on.
However, Delap’s hamstring injury midway through the half disrupted the Blues’ rhythm.
Fulham capitalised and thought they had taken the lead when 18-year-old Josh King finished off a counter-attack for what would have been his first Premier League goal.
The celebrations were short-lived, though, as VAR judged Rodrigo Muniz to have fouled Trevoh Chalobah in the build-up.
Marco Silva was furious on the touchline, protesting the decision. "That is a big moment in the match," Silva said afterwards. "We feel hard done by because it could have changed the game completely."
Chelsea’s breakthrough came late in the first half. Bernd Leno denied Tyrique George with a sharp stop, but from the resulting corner Enzo Fernandez’s delivery was met by Joao Pedro, who powered in a header. It was a rare moment of quality in an otherwise tense first period.
After the interval, VAR played a decisive role once more. Chalobah’s cross struck the arm of Ryan Sessegnon inside the area, and following a pitchside review, referee Rob Jones pointed to the spot.
Fernandez stepped up and confidently converted, doubling Chelsea’s advantage. From that point, the home side controlled proceedings, and Pedro might have added a third when through on goal, only to hesitate and allow Leno to close him down.
Despite the win, Maresca admitted his side still have work to do. "The first half was not good enough, we were slow and predictable," he said. "But we showed resilience, and in the end we got the result. That is what matters."
Fulham will leave west London still searching for their first league win of the campaign.
Arne Slot praised Dominik Szoboszlai's "unbelievable" display after the midfielder, once again filling in at right-back, struck a sensational late free-kick to hand Liverpool a 1–0 victory over Arsenal at Anfield.
Chelsea striker Nicolas Jackson has defied club orders to return to London after the club abruptly cancelled his loan move to Bayern Munich - a decision that has left the player furious and hoping to revive the deal before the transfer window closes.
Reports coming out of England and Germany suggest RB Leipzig could approach Liverpool with a bid to sign Harvey Elliot.
Chelsea have completed the signing of Alejandro Garnacho from Manchester United, with the Argentina international putting pen to paper on a long-term deal at Stamford Bridge that runs until 2032.
