The Belgium forward set up the Blues’ opener with a wonderful pass across the face of goal for the arriving Pedro to tap in on 17 minutes.
Willian then pounced on a loose pass from Leon Balogun and played in Hazard, who ran from just over the halfway line, outpacing the Brighton defence, before slotting past Mat Ryan just after the half hour mark.
Brighton, who welcomed back Glenn Murray to the starting XI after a shoulder injury, barely threatened in the first hour.
But they improved following Murray’s substitution for Romanian striker Florin Andone and pulled a goal back in the 66th minute.
Bernardo headed a cross back across goal and Solly March was unopposed as he hooked his shot past Chelsea keeper Kepa Arrizabalaga
Seagulls fans felt Marcos Alonso should have been sent off as last man after fouling March late on, but the Spaniard was shown a yellow card instead.
Chelsea withstood the hosts’ late attacks to record their first away win in three games to stay in fourth in the Premier League, two points behind Tottenham.
Brighton remain in 13th place.
