Chelsea manager Maurizio Sarri said Claudio Ranieri can "have a very great impact" at Fulham after his team overcame a spirited Cottagers side to claim a valuable victory at Stamford Bridge.
Ranieri was appointed Fulham boss on 14 November after Slavisa Jokanovic was sacked and the Italian guided his new team to victory over Southampton in his first game in charge last Saturday.
However, despite a brave second-half performance, his Cottagers were unable to breach the Chelsea defence and they fell to defeat through goals from Pedro and Ruben Loftus-Cheek either side of the break.
"Today was about the result - we gave more attention to the defensive phase to get the win," Sarri told Sky Sports.
"Now we have to start to improve and play our football in a better way.
"Ranieri can have a very great impact at Fulham, in two or three weeks they will defend very well and in a month, playing against them will be a problem for any team."
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 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.
Ranieri, who managed Chelsea between 2000 and 2004, believed his team deserved a draw.
"We wanted to play football but we made mistakes and against big champions you pay everything for that," Ranieri told BBC Sport.
"In the second half we changed system and maybe we deserved to draw the match. I am satisfied with how my players made decisions with the ball. We played together strongly and created good chances."
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.
Before Sunday's game, the Cottagers had claimed just one point from a possible 21 in away games this season, and disappointingly for new boss Ranieri, they were unable to buck the trend at Stamford Bridge.
There were promising moments for the visitors early on, even after Chelsea's first goal, but neither Cyrus Christie nor Calum Chambers could seriously test Kepa Arrizabalaga, shooting straight at the Spaniard.
But it was only after Ranieri introduced Aboubakar Kamara and Floyd Ayite at half-time that his side began to pose a serious threat.
Kamara's low cross was nearly deflected into the Chelsea net by Antonio Rudiger, and Kepa had to make a fine save to keep out Chambers' header from the resulting corner.
And the Arsenal loanee drew another good save from Kepa shortly after, as the Spaniard dived to his right to beat away Chambers' curling effort.
However, despite the Cottagers' best efforts, they were unable to put their hosts under a sustained period of pressure, and Chelsea held on to claim consecutive home clean sheets for the first time this season.
Meanwhile, Fulham are the only side in England's top four tiers who are yet to keep a clean sheet in 2018-19.
Deployed in central midfield, Calum Chambers was Fulham's top performer. He made seven tackles, three interceptions and took three shots on goal, more than any of his team-mates in each instance
Chelsea manager Maurizio Sarri on BBC Sport: "We can't do much about the game against Tottenham - we played very badly and lost the game. Today was difficult, we started well and we had a good level of application.
"We created some opportunities for 2-0 but missed them - we were in control of the match and I was afraid only because I saw that the team were a bit tense. The last 15 minutes could have been a problem but then we scored.
"Ruben Loftus-Cheek played very well in the Europa League and I am very happy with him. Today Mateo Kovacic had a knock to his ankle so he came on, it is not a problem to play with him. He is improving and he will be very important for us in the future."
Fulham manager Claudio Ranieri to Sky Sports: "We played so so in the first half, we made a mistake for the first goal but we were much better in the second. We made chances but when you play big champions they can do that. It was a positive match for us, we are improving.
"It will be very emotional for me to play Leicester on Wednesday, but it is very important for us. I am positive."
Chelsea leave it late (again) - the stats
Chelsea travel to Molineux to face Wolves on Wednesday, 5 December (19:45 GMT), and Fulham host Leicester the same day (19:45).