25. Vito Mannone 2. Phil Bardsley 16. John O'Shea 5. Wes Brown 3. Andrea Dossena 4. Ki Sung-Yueng 23. Emanuele Giaccherini 65' 8. Craig Gardner 80' 14. Jack Colback 57' 31. Fabio Borini 17. Jozy Altidore Subs: 7. Sebastian Larsson 57' 9. Steven Fletcher 80' 11. Adam Johnson 65' 12. Ondrej Celustka 13. Jordan Pickford 29. Valentin Roberge 33. Lee Cattermole
The Belgium international was both provider and scorer on the night, producing the cross from which Frank Lampard cancelled out Jozy Altidore's opener and then two pieces of individual magic to effectively win the game.
Victory on Wearside helped second-placed Chelsea to maintain the pressure on Barclays Premier League leaders Arsenal despite falling behind for the third time in as many games.
However, it left Sunderland deep in trouble despite a spirited performance as manager Gus Poyet's run of three successive home victories in all competitions came to an end in front of a crowd of 40,652.
Hazard's intervention was vital for Jose Mourinho's men with Altidore having given the Black Cats a 14th-minute lead with his first league goal for the club.
However, Chelsea's response was concerted with Juan Mata, Lampard, and Ramires all influential, and they were back on terms barely before the home fans had stopped celebrating through Lampard's fifth goal of the season, a close-range header.
But it was Hazard who stole the show, capping a fine individual first-half display with an enterprising 37th-minute run and sumptuous finish to restore order.
John O'Shea dragged the home side right back into it five minutes into the second half when Chelsea made a hash of clearing Emanuele Giaccherini's less-than-sweetly-struck corner, and the defender helped it into the net to rekindle his side's hopes.
But Hazard was not done and it was he who ensured that the points headed south when he took it upon himself to leave defenders in his wake once again to rifle a 62nd-minute shot past keeper Vito Mannone.
There was late drama as full-back Phil Bardsley scored at both ends inside a minute, but the outcome remained the same.
Fourteen years ago to the day, Poyet, then wearing the blue of Chelsea, heading for the away dressing room at the Stadium of Light wondering what had hit him with his side trailing 4-0.
This time around, he found himself on the other side of the corridor facing the task of lifting his players after seeing them take the lead, only for the visitors to mount a powerful fightback.
The Black Cats had slipped back to the foot of the table without kicking a ball on Tuesday evening as a result of Crystal Palace's 1-0 win over West Ham, and they emerged determined to do all they could to address that situation in the most trying of circumstances.
Their initial efforts could not be faulted as they took the game to the Blues with Giaccherini forcing a first-minute block from Cesar Azpilicueta and Fabio Borini sending a cross across the face of goal seconds later.
But keeper Petr Cech was eventually beaten with 17 minutes gone when, after Andrea Dossena's tame free-kick had come back of the wall, Jack Colback slipped the ball to Altidore and he span John Terry before blasting a left-foot shot past the helpless Cech.
The lead, however, lasted just three minutes when, after Sunderland failed to deal fully with Juan Mata's corner, Hazard recycled the ball, wrong-footed Bardsley and crossed for Lampard to head home unopposed.
Sunderland refused to be cowed by Mourinho's men despite their freedom of movement in midfielder, and with Altidore ruffling the feathers of Terry and Gary Cahill and Dossena providing a useful outlet down the left, pressed once again.
Cech had to turn away Dossena's stinging 31st-minute effort, which may have been going wide anyway, but opposite number Mannone was not so fortunate six minutes later.
Fernando Torres helped on a long clearance to Hazard on the left and he cut inside past Bardsley and the covering Craig Gardner before firing across the Italian and into the far corner.
But Sunderland refused to give up and they were back on terms within five minutes of the restart when Giaccherini's skidding corner was allowed to reach O'Shea, who swept it past Cech to level.
Chelsea should have been back in front seven minutes later when Ramires robbed Jack Colback and fed Torres, who in turn picked out Hazard in space.
He slid past O'Shea and Ki Sung-yueng with ease before unleashing a shot which Mannone managed to beat away to Torres, who skied his follow-up high over.
But it was Hazard who did the trick once again with 62 minutes gone, collecting Lampard's intelligent back-heel and rounding O'Shea before beating the helpless Mannone with ease.
Bardsley turned substitute Demba Ba's cross into his own net six minutes from time, but then converted Sebastian Larsson's corner at the other end seconds later, although ultimately to no avail.