Yves Bissouma scored his first goal for the Seagulls with a stunning strike from 25 metres out in the 20th minute.
The midfielder unleashed a curling shot past the outstretched arms of keeper Nick Pope to nestle in the top corner and give Brighton an early lead.
Burnley restored parity in the 44th minute as striker Chris Wood expertly latched on to a through ball to finish past Ryan to make it all square going into the half-time break.
But Brighton didn’t take long to make their mark again in the second half, as Aaron Connolly netted from a tight angle to give the Seagulls the lead again.
The Clarets appeared to equalise yet again in the 58th minute from a corner but had the goal eventually ruled out by VAR as the game ended 2-1 to Brighton.
Socceroos midfielder Aaron Mooy made an appearance late in the game as a substitute in the 73rd minute, his best involvement coming when he flashed a shot past the post in stoppage time.
The win gives Brighton their best Premier League points tally yet, a club record 41 points to finish the campaign in 15th place to safely avoid relegation.