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.
9. Chris Wood 5.5
The New Zealander's only attempt of note trickled harmlessly into the arms of Sanchez. Provided the Clarets with a good out-ball on occasions, but appeared fatigued after a summer with the OlyWhites in Japan.
10. Ashley Barnes 5
Replaced Rodriguez with 20 minutes remaining, but unable to make an impact. His first touch often let him down and both Dunk and Duffy marshalled the substitute with relative ease.
11. James Tarkowski 7
Gave Burnley the lead with a second minute header and almost had a second when acrobatically firing a rebound over the bar after Mee had hit the bar. Showcased his physical prowess in battle with Maupay, with both players booked in the first half.
12. Johann Berg Gudmundsson 6.5
Incredibly unfortunate to see his first half effort come back off the inside of the post. Alert, decisive and incisive throughout, partnering effectively with Lowton. Necessity to cut back onto stronger foot remains a limitation.