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.
9. Jack Cork 7
His contribution perhaps won't get the acknowledgement it truly deserves, as the 'dirty' work sometimes goes unnoticed, but he played an integral part in victory. Dogged, determined, diligent. He showed great strength on the ball and suffocated the opposition to keep Lallana and Bissouma quiet.
10. Maxwel Cornet 6
Didn't quite get the breaks at Brighton when restored to his number 10 role, but stuck to his task while showing signs that his partnership with Weghorst is still simmering. Worked well across the front, won several corners, but limped off injured in the second half.
11. Wout Weghorst 8.5
The man is a machine! Another sterling display up front from the Netherlands international. Great with his feet, holds the ball up well, good strength and gets stuck in. Opened his account with a stunning first-time finish and laid on the second for Brownhill.
12. Jay Rodriguez 7
Perhaps a tad unfortunate to be sacrificed from the starting XI, but showed a tremendous attitude when introduced. Made a real impact for the final 35 minutes, battling tenaciously for the ball, and demonstrated good physicality and awareness to set up Lennon for the third goal.