The Belgian struck twice to inspire the Blues to victory after a seven-goal thriller which also saw Jozy Altidore and Frank Lampard score and Phil Bardsley net at both ends.
The 22-year-old put in a man-of-the-match performance against the Black Cats, netting in both halves as Chelsea earned its ninth straight victory over Sunderland at the Stadium of Light in the Premier League after a seven-goal thriller.
American striker Jozy Altidore opened the scoring on his return to the Sunderland side with a fierce shot, but Frank Lampard's close-range header soon restored parity.
The superb Hazard put Chelsea ahead in the first half with an angled drive before a rare goal from John O'Shea once more leveled the scores on 54 minutes.
But Hazard restored the lead with a fine individual effort, before Phil Bardsley scored at both ends as Chelsea racked up three straight top-flight victories, while Sunderland remains rooted to the foot of the table with eight points.
Sunderland brought in Altidore and Jack Colback for Steven Fletcher and Sebastian Larsson, while Chelsea also made changes with Lampard and Willian coming in for Michael Essien and Oscar.
Chelsea fired an early warning shot when Lampard shot wide from 25 yards, but it was the home supporters who were on their feet celebrating after 14 minutes.
Andrea Dossena's free kick rebounded into the path of Colback and his pass found Altidore, who turned John Terry in the box and fired home a left-footed effort.
Undeterred by the setback, Chelsea sought an immediate response and Jose Mourinho's side was rewarded just three minutes later.
Juan Mata burst into the box before cutting onto his right foot and lofting a pinpoint cross for Lampard to apply the header from inside the six-yard box.
Buoyed by the equalizer, Chelsea continued to look threatening, but was largely frustrated by a resolute Sunderland defense until Hazard found the breakthrough on 36 minutes.
The Belgium international received the ball on the left and drove at the Sunderland defense before striking a fierce low effort into the far corner beyond Vito Mannone.
Gus Poyet would have been happy with the fight his Sunderland side showed in the first half and his charges found an equaliser against the run of play shortly after the break.
Chelsea failed to deal with Craig Gardner's corner and O'Shea swept home to level.
Mourinho was visibly frustrated on the sidelines and his mood should have been lifted when Hazard's shot was parried into the path of Fernando Torres, but the Spain international blazed over the crossbar.
But Chelsea scored a third goal in the 62nd minute to mark the third Premier League game running in which it has scored three or more. Hazard played a neat interchange with Lampard before rounding two defenders and driving past a helpless Mannone.
Demba Ba was introduced from the bench and his low cross was turned home by the unfortunate Bardsley to open up a two-goal lead, but the former Manchester United defender turned in a corner with four minutes remaining to reduce the damage for Sunderland.