First-half goals from Leandro Trossard and Neal Maupay snapped the Seagulls' 11-match winless run while the Bees slipped to a second straight defeat following a midweek loss to Chelsea in the Carabao Cup.
Brighton scored twice in a six-minute span late in the first half through Trossard's lovely chip over Alvaro Fernandez and leading scorer Maupay with a curler against his former club for his seventh of the season.
Story of the match
The hosts settled into the contest and in the 18th minute, Mac Allister's corner found the head of Burn, but he sent his shot onto the top of the bar.
Continuing to dictate play, Brighton made the breakthrough when Trossard timed his run perfectly to get on the end of Enock Mwepu's pass and the Belgian volleyed over an onrushing Fernandez.
The lead was doubled after Lallana won the ball up high, passed to Jakub Moder, who found Maupay 25 yards. The Frenchman advanced the ball and his effort found the top right corner, having now scored in three straight games.
Mac Allister nearly made it three with a low drive that was only inches wide of the post. Marc Cucurella then cleared Baptiste's looping header from under the bar.
Man of the match: Enock Mwepu
He assisted on Brighton's opening goal, but the Zambian was particularly excellent in the middle of the park, disrupting Brentford every time they had possession. Was a tireless worker and ran well into attacking areas.