The 22-year-old put in a man-of-the-match performance against a spirited Sunderland side, netting in both halves as Chelsea earned their ninth straight victory over Sunderland at the Stadium of Light in the Premier League in an exhilarating fixture.
Jozy Altidore had opened the scoring on his return to the Sunderland side with a fierce strike, 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 levelled 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 remain 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 fired 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-foot effort.
Undeterred by the setback, Chelsea sought an immediate response and Jose Mourinho's side were rewarded just three minutes later.
Juan Mata burst into the box before cutting onto his right foot and lofting a pin-point cross for Lampard to apply the header from inside the six-yard box.
Buoyed by the equaliser, Chelsea continued to look threatening, but were largely frustrated by a resolute Sunderland defence until Hazard found the breakthrough on 36 minutes.
The Belgium international received the ball on the left and drove at the Sunderland defence 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 did score a third goal for the third Premier League game running on 62 minutes as 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 arrears for Sunderland.
