Winger Anthony Knockaert fired the Seagulls ahead early on, with a low 20-yard effort into the corner.
Sam Baldock slotted the ball in to double the lead just before the break.
Matej Vydra headed against the outside of the post for Derby, before Glenn Murray bundled in his 18th goal of the campaign from Knockaert's cross to seal Brighton's 14th home win of the season.
The Seagulls remain second in the table with an inferior goal difference to Newcastle, but now have a nine-point buffer to Huddersfield in third - albeit the Terriers have two games in hand.
Of their nine matches left, eight are against sides in the bottom half of the table as they look to return to the top flight for the first time since 1982-83.
Following a trip to play-off chasing Leeds next Saturday, April's fixture list is kind to Chris Hughton's men with home games against Blackburn, Birmingham, Wigan and Bristol City.
Their outstanding frontline of Murray, Baldock and Knockaert have now scored 42 Championship goals between them this campaign, and gave Derby's defenders a torrid time with their pace, movement and clinical finishing.
Former Leicester forward Knockaert was instrumental in most of Brighton's attacking play, bending home a superb effort to open the scoring and seeing Scott Carson tip over his fierce second-half strike.
The Rams started with former England pair Darren Bent and David Nugent up front, but Brighton's defence were rarely troubled in keeping their 19th clean sheet of the season.
Derby, who are 10th and 10 points behind sixth-placed Sheffield Wednesday, have now only picked up six points from their past nine matches and their play-off hopes appear to be over for another season. - BBC -