Solly March pulled one back for the hosts to set up a tense finale, but Chelsea held on to move three points clear of fifth-placed Arsenal courtesy of the Gunners' shock 3-2 defeat at the hands of struggling Southampton.
Maurizio Sarri was able to welcome a host of first-team players back into his side after resting them in midweek, returning to the same XI which inflicted a first league defeat of the season on Manchester City last weekend.
Hazard was therefore utilised in a false nine role once again, and he caused the Brighton defence problems within six minutes when he won a free kick which David Luiz fired into the arms of Mathew Ryan.
Brave blocks at either end denied March and then Marcos Alonso from breaking the deadlock before the opener did arrive through a moment of magic from Hazard, although Brighton were left to bemoan the lack of an offside flag against Alonso.
Hazard saw his initial effort blocked but picked up the loose ball and drove into the area before playing an incisive low pass across the six-yard box for Pedro to tap in at the back post.
Replays showed that Alonso was standing in an offside position as the ball passed in front of him, though, and Ryan's dive suggested that the Spaniard was interfering in play despite not touching the ball.
Brighton were struggling to create anything of their own going forward, and their best attacking moment of a disappointing first-half performance saw March draw a low stop from Kepa Arrizabalaga with a powerful strike from range.
By the same token the Seagulls were not giving much away to Chelsea, at least until the second goal when Leon Balogun's misplaced pass was ruthlessly punished as Willian released Hazard through on goal and the Belgian made no mistake with his finish.
The hosts almost added a third with just four minutes remaining until the interval as Antonio Rudiger met Willian's corner with a thumping downward header, but his effort bounced inches past the post.
Another opening went begging four minutes after the restart too as Cesar Azpilicueta's low pass into the box was missed by Hazard, and neither N'Golo Kante nor Pedro could hook it on target from the follow-up.
Alonso was the next to come close for the visitors just past the hour mark, but this time it was the woodwork which came to Brighton's rescue as the Spaniard's whipped long-range strike crashed against the inside of the post with Ryan reduced to a spectator role in goal.
It looked as though Chelsea might be made to rue those missed chances when Brighton pulled a goal back moments later, with Bernardo turning a deep cross back into the middle and March reacting quickest to fire the ball home from close range - the Seagulls' first goal against Chelsea since 1983.
Not since 1967 have Brighton avoided defeat against the Blues, but all of the late pressure came from the home side and Alonso was fortunate to avoid a late red card when he tugged March back to deny the Albion goalscorer a clean run through on goal.
March fired the resultant free kick well over the bar himself, and the only other half-chance Brighton created was a Lewis Dunk header which bounced wide of the target as Chelsea held on.
The result leaves Sarri's side still just two points behind London rivals Tottenham Hotspur but crucially opens up a gap to fifth place as Chelsea record back-to-back league wins for the first time since the beginning of November, inflicting just a second home league defeat of the season on Brighton in the process.
BRIGHTON (4-4-1-1): Ryan; Montoya, Balogun, Dunk, Bernardo; Knockaert (Locadia 83') Propper, Stephens, March; Gross (Bissouma 81'); Murray (Andone 60')
CHELSEA (4-3-3): Kepa; Azpilicueta, Rudiger, Luiz, Alonso; Kante, Jorginho, Kovacic (Barkley 75'); Pedro (Loftus-Cheek 66'), Hazard (Giroud 83'), Willian