The Clarets were off to the perfect start when James Tarkowski brushed off Neal Maupay to guide Ashley Westwood's corner beyond Robert Sanchez with just two minutes played.
Sean Dyche's side continued to dominate and deserved to be out of sight at the break.
Johann Berg Gudmundsson showed good feet to work a shooting opportunity, only to see his right-footed effort come back off the inside of the post.
Ben Mee's header then bounced down on to the line via the underside of the crossbar after Sanchez flapped at another Westwood set-piece, while Tarkowski acrobatically fired the rebound over.
You wondered whether the Seagulls would make their hosts pay for their missed opportunities after the break — and they did!
Boss Graham Potter rang the changes and all three — Adam Lallana, Jakub Moder and Alexis MacAllister — made an impression.
The Polish midfielder slid the ball into Maupay, who levelled in the 73rd minute from close range.
And Argentinian substitute McAllister steered home the winner five minutes later in what was a carbon copy of the equaliser, only Pascal Gross provided the assist on this occasion.
Here are the player ratings.
1. Nick Pope 6
Could've watched the game from the stands for the first hour, but beaten twice in similar fashion in the final 20 minutes. Almost conceded a third late on, only for James Tarkowski to intervene on the line.
2. Matt Lowton 6.5
Looked at ease on the ball, cutting through players effortlessly at times. Combined well with Gudmundsson to manufacture crossing opportunities down the right hand side. However, slightly culpable for Brighton's equaliser.
3. Ben Mee 6.5
Went excruciatingly close to doubling Burnley's lead when his header dropped onto the line off the underside of the crossbar. Defended well on the whole, affording the visitors very little time and space on the edge of the box.
4. Charlie Taylor 6.5
A real menace in the first half, linking up well with McNeil to get beyond March and Webster. Carried the ball exceptionally well at times after the break, but both Brighton goals came from down his side of the pitch.