Gonzalo Higuain and Jorginho were on target as Chelsea handed Scott Parker a losing start as Fulham caretaker boss.
Moments after the recalled Kepa Arrizabalaga almost presented Fulham with a goal by dropping a straightforward cross, Higuain put the visitors in front with just his third Blues goal since his January arrival on loan from Juventus.
Calum Chambers equalised, but Jorginho restored Chelsea's lead just three minutes later with his second goal for the Blues. It proved to be enough, although Ryan Sessegnon had a stoppage-time effort ruled out for offside.
Parker replaced the sacked Claudio Ranieri this week and will be under no illusions at the size of the task facing the Cottagers, who are now 10 points adrift of safety with nine games to go.
But Chelsea did not take full advantage of the chances created as Higuain, in particular, missed opportunities to improve his goal tally. Sixth-placed Chelsea have a game in hand and are now a point behind fifth-placed Arsenal and two adrift of Manchester United in fourth.
Kepa replaced Willy Caballero following his demotion to the bench in the midweek win over Tottenham for his refusal to be substituted in last Sunday's Carabao Cup final penalty shoot-out loss to Manchester City.
His inclusion was one of five Blues changes, while Parker made one change from Ranieri's last line-up, with Sessegnon starting in place of Andre-Frank Zambo Anguissa.
Fulham had not kept a clean sheet in nine games in 2019, not since the 29 December defeat of rock-bottom Huddersfield.
Higuain's only goals in seven prior Blues appearances were against the Terriers and he should have added to his double that day after four minutes, but he headed wide from an Eden Hazard cross.
Fulham responded. Kepa almost added to his recent list of misdemeanours when he dropped Kevin McDonald's regulation cross with Ryan Babel lurking, as two Chinook helicopters travelled noisily overhead.
Fortunately for Chelsea the goalkeeper was the more alert and gathered the loose ball.
The Blues led soon afterwards, Cesar Azpilicueta overlapped on the right and his cross was tucked in by Higuain.
Fulham fought back, as Sessegnon's cross flicked up off Azpilicueta and Aleksandar Mitrovic improvised to volley towards goal. Kepa made a fine instinctive save, but he was beaten from the resulting corner.
Babel's cross following a short corner found Chambers at the far post. Unmarked, the on-loan Arsenal man volleyed in.
Fulham soon found themselves behind again however as Hazard sucked in defenders and laid the ball back for Jorginho to pass the ball into the top corner from the edge of the area.
Fulham were fuming, believing Jorginho fouled Joe Bryan earlier in the move, but referee Graham Scott ignored the complaints. It was Jorginho's second goal for Chelsea, following his penalty on the opening day of the season at Huddersfield.
Jorginho, who leads the Premier League passing statistics, thought he had his first assist after floating a pass for Higuain. Instead, the Argentina striker blasted over.
Higuain was next denied by Fulham goalkeeper Sergio Rico on the stroke of half-time in a move which was a copy of his goal. Higuain was absent from the six-yard box when Hazard sent the ball across goal after Bryan's sliced clearance early in the second half.
All it needed was a touch and Chelsea would have had their two-goal cushion, but the failure to find a third made for a shaky finale.
Mitrovic curled just over after Andreas Christensen's failed interception and next Kepa saved from Tom Cairney.
Kepa saved from Mitrovic in the 88th minute as the striker headed Floyd Ayite's cross goalwards. Sessegnon thought he had equalised in stoppage time, only for the strike to be ruled out for offside and Fulham's chance of a welcome point was over.