Gonzalo Higuain and Jorginho were on target as Chelsea won 2-1 at Craven Cottage to hand 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.
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.