A fine early goal from Sam Baldock put the Seagulls on their way to a fourth successive win before a Glenn Murray penalty and an Anthony Knockaert strike extended Albion’s unbeaten run to 17 games.
Struggling Rangers, reduced to 10 men early in the second half when captain Nedum Onuoha received a straight red card, have now lost their last six matches and failed to score in five of them.
Albion, now eight points clear of third-placed Reading, made the perfect start before a crowd of 30,176 with Baldock putting the hosts in front after only 11 minutes.
The former Bristol City striker finished emphatically with his left foot into the top corner from 20 yards.
Skipper Bruno had won possession from a Rangers throw-in and Murray slipped the ball to Dale Stephens who then fed Baldock.
Baldock had begun in lively fashion hitting two snap shots wide for Brighton, who had made two changes with Solly March replacing Jiri Skalak and Oliver Norwood coming in for Steve Sidwell.
Rangers came close to equalising midway through the half when a goal-bound shot from Massimo Luongo was well saved by David Stockdale after a poor clearance by Norwood.
Seagulls striker Murray, with eight goals from his previous eight games, should have hit the target when heading wide at the far post after Shane Duffy headed down a Norwood corner.
Brighton had a let-off on 33 minutes when defender Jake Bidwell crossed accurately for Idrissa Sylla who got in between two defenders at the far post but shot wastefully wide.
Ending the right way
Brighton took a firm grip of the game eight minutes after the interval when top scorer Murray doubled their lead from the penalty spot with his 15th goal of the season.
Murray, on a season-long loan from Bournemouth, made no mistake by slotting his 13th goal at the Amex after a reckless challenge by Luongo on Stephens.
Rangers were reduced to 10 men on 56 minutes when Onuoha received a straight red card from referee Keith Stroud for bringing down the on-rushing Baldock on the edge of the area.
French winger Knockaert made it 3-0 in the 69th minute with a low left-footed strike after being set up by Stephens.
It was an emotional moment for former Leicester man Knockaert, who celebrated by holding aloft a picture of his late father Patrick who passed away recently.
Albion keeper Stockdale, who claimed a 14th clean sheet, saved superbly to deny Sylla after Alex Smithies had kept out efforts from Stephens and substitute Jamie Murphy at the other end.