Hazard and teammate Willian had the reigning Premier League champions two goals ahead within six minutes before the Belgium playmaker added another and Victor Moses netted near the end to take them above third-place Liverpool in the table.
Seagulls boss Chris Hughton, yet to see his side take a point from any of the top six, reverted to a back five against the Blues -- but it was soon apparent they would not be breaking their duck just yet.
Only three minutes had elapsed when Moses reached the byline and his cut-back found its way to Hazard, who sidestepped Lewis Dunk before firing home.
And three minutes later Hazard and Michy Batshuayi combined in a blur of backheels before Willian provided the finish from just inside the area.
It was a stunning goal and ruthless stuff from a Chelsea side who had scored only once in their previous four matches.
They were hit by injuries to four players as well as bans for Alvaro Morata and Pedro following Wednesday night's chaotic FA Cup tie against Norwich.
But for a spell the Blues looked as though they would score every time they went forward with Hazard leading the charge, teeing up first Willian and then Batshuayi whose efforts were saved by Mathew Ryan.
To their credit, Brighton had their moments in the first half, too. They had two decent penalty shouts for trips on Ezequiel Schelotto, first by Blues keeper Willy Caballero -- in for the injured Thibaut Courtois -- and then Tiemoue Bakayoko.
With the video assistant referee (VAR) system Chelsea felt so hard done by in midweek not in place, referee Jonathan Moss waved away both appeals and booked the Brighton full-back for his protests after the second one.
Shortly after the interval Brighton were inches from halving the deficit when Davy Propper's header beat Caballero but came back off the post.
Chelsea lost defender Andreas Christensen to a head injury after he tried to play on despite looking very dazed following a clash in the penalty area.
Moments later it was Brighton who were grateful to the woodwork, and Ryan, who did well to palm Willian's goal-bound free-kick against the upright.
But Hazard put the game to bed 13 minutes from time when he ran unchallenged into the Brighton area before sweeping the ball past Ryan.
And with full-time approaching substitute Charly Musonda's fine ball sent Moses clean through to slide in number four and seal an emphatic return to winning ways.