The victory was the Clarets' first on the road this season and their first success in the top flight since late October when beating Brentford at Turf Moor.
The visitors almost got their noses in front when Connor Roberts' left-footed effort from the angle of the penalty area, after cutting past Alexis MacAllister, beat goalkeeper Robert Sanchez all ends up, but came back off the crossbar.
However, the Welshman turned provider just before the midway point of the half when pulling the ball back for Wout Weghorst, who struck first time, beating Sanchez at his near post, to open his account for the club.
The deadline day signing from VfL Wolfsburg added an assist to his repertoire five minutes before the break when teeing Josh Brownhill up for his first goal in the Premier League.
The midfielder shifted the ball on to his left foot inside the area and his shot squirmed past the Seagulls' Spanish stopper via a touch off Marc Cucurella.
Aaron Lennon rounded off a fine afternoon in Falmer in the 69th minute when substitute Jay Rodriguez stabbed the ball into his path and the ex-England international fired home off the underside of the crossbar.
Here are the ratings.
5. Ben Mee 7.5
The skipper led his defence superbly. Distributed the ball well across the back when Brighton pressed, telegraphed passes and stole possession, and made an excellent challenge to thwart Mac Allister, while getting hurt in the process. His performance added to the anonymity of Welbeck and Maupay.
6. Aaron Lennon 8
Rolled back the years with a non-stop, all-action display at the AMEX. Played a significant hand in the opener, when supplying the pass for Roberts, worked tirelessly up and down the pitch, keeping Cucurella occupied, and rounded off the win with an outstanding finish.
7. Dwight McNeil 7.5
Slowly starting to rediscover his form at the perfect time for Burnley. Productive in possession, knowing when to keep the ball and when to offload, carried it purposefully, worked hard against the ball to negate Lamptey's threat, and played with a smile on his face again.
8. Josh Brownhill 8
Like a man possessed! Magnificent once again in the middle of the park; winning the ball in key areas, linking the play, typically working hard out of possession and, after a long wait, deservedly scored his first Premier League goal for the club.