Fulham were denied a late stoppage-time Ryan Sessegnon equaliser, as first-half goals from Gonzalo Higuain and Jorginho either side of a Calum Chambers leveler, sealed the full points for Maurizio Sarri's Chelsea in the west London derby at Craven Cottage.
After Higuain had opened the scoring on the Thames, both goalkeepers produced a number of smart saves to deny their opponents, as Kepa Arrizabalaga won back the visiting fans to deny striker Aleksandar Mitrovic on a number of occasions.
Cottagers' caretaker boss Scott Parker would have been pleased by what he saw and reaction his players made after going from behind, but ultimately another defeat for the hosts leaves the Whites still deep in trouble at the foot of the Premier League standings.
In Parker's first game as caretaker boss in the Cottagers dugout, the former Chelsea man himself saw his side began nervously, but nevertheless were finding space on the flanks.
Indeed in the early minutes, Ryan Babel's cross found Tom Cairney in his more accustomed number ten role, only for Cesar Azpilicueta to make a vital block away from danger in the penalty area.
The hosts almost drew first blood when Kepa - returned to Sarri's starting XI after the Spaniard's infamous substitution altercation in last weekend's Carabao Cup final - narrowly avoided gifting Fulham the lead.
After a seemingly harmless ball into the box, Kepa fumbled the ball behind him. With Babel in close attendance, the Dutch winger could not re-adjust his position as the Blues 'keeper escaped to grab the ball back.
Higuain ignites derby
Chelsea were slowly coming into the game and Higuain was finding increasing amounts of space up top. The link up with former Napoli teammate Jorginho was bearing much promise, but it was the raiding runs of Azpilicueta that opened the scoring in the 20th minute.
As the full-back sauntered forward down the right channel, the Spaniard's cut inside a hapless Fulham back line and crossed low for Higuain to notch his fourth goal for his new club.
The hosts responded well and were only denied a leveler by Kepa's reflex save to tip over Mitrovic's thumping left-foot effort. From the resulting corner however, the Whites did pull level.
It was again Babel who was providing the threat for Parker's side and as the corner was played short, his cross found Chambers in yards of space at the far post to side-foot volley home from inside the area.
Chelsea continued to see most of the ball however and four minutes late were back ahead. Hazard was this time the conductor of the Blues' band, and his cutback found Jorginho from the edge of the box to curl an effort sweetly into the top corner.
Higuain should then have made it three but blazed over from Jorginho's lofted ball over the Fulham defence. Goalkeeper Sergio Rico was keeping the hosts in the game in truth and made two important saves both from Hazard and again from Chelsea's Argentine marksman in first-half stoppage time as the Cottagers clung on for the break.
Blues seek early conclusion
The visitors came out for the second period intent on putting the game to bed early on, and Rico made a handful of comfortable saves, with Willian also shooting narrowly wide of goal after a long ball forward.
Hazard and Ross Barkley were seeing more and more of the ball in the middle of the park and the former was edging his way into pockets of a Fulham defence that was beginning to creak.
A growing blue tide continued to build, but Fulham were not reduced to just occasional counter-attacks. The Cottagers came close to an albeit unlikely equaliser as Mitrovic thundered a shot inches over the bar on the hour-mark.
Indeed as the second half ticked on, the men in white sought to get a foothold back in the game, as Kepa this time was forced to make a smart stops from Mitrovic and Joe Bryan.
Hosts denied late leveler
As the game moved into the final fifteen minutes, somewhat of a lull in proceedings fell upon the Thames, with the game still on a knife-edge, as Chelsea's nerves from their recent outings begins to appear in their play.
Fulham made their last roll of the dice to grab derby spoils with Luciano Vietto coming on, and his introduction saw the hosts garner more room in the middle of the park.
Together with fellow substitute Floyd Ayite, the latter flicked a long ball on to Mitrovic with only minutes to go, only for Kepa to once more deny the Serbian from a sensational late strike.
Then, with the game deep in stoppage time, the hosts were denied a dramatic derby leveler. After a hopeful ball was lofted into the area, the ball dropped to Sessegnon who stole in sweep the ball into the Chelsea net, only for the winger to be adjudged to be marginally offside.
It was a final scare for the Blues who clung on to take full derby spoils and climb back into the battle for a top four finish. Fulham meanwhile remain mired in relegation trouble.