The lead, however, lasted just three minutes as Blues veteran Frank Lampard slotted home from six yards when he was found by Hazard's cross after a Juan Mata corner.
The provider then turned scorer just after the half-hour mark when he evaded two would-be tacklers before firing home form the edge of the area to give Chelsea a 2-1 lead.
Five minutes into the second half, Sunderland captain John O'Shea fired home Emanuele Giaccherini's corner, via Wes Brown, to level the scores but Chelsea were intent on getting back in front and did so just after the hour-mark when Hazard rifled home a second after a neat exchange with Lampard.
The Blues then were granted some breathing space in the 84th minute when Phil Bardsley turned in Demba Ba's low cross to give the home side a 4-2 advantage before Bardsley atoned for his error by giving the Black Cats hope when finishing from close range just minutes later.
However, there was not enough time for Sunderland to rally for a late equaliser as they remained rooted to the bottom of the table while Chelsea were busy putting together a winning run of three league games.
2013/14 Premier League scores
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