Burnley finish the season in 10th place on 54 points while Brighton, who had flirted with relegation, conclude in the safety of 15th place.
But Burnley drew level just before the break when Chris Wood got behind the Brighton defence to collect a diagonal ball from Erik Pieters and the New Zealander slotted home with a cool, left-foot finish.
"He had a chance to get a share of the golden glove, and a worldie is their first goal and it was a soft second from us defensively in front of him," said Burnley manager Sean Dyche.
"I would have liked to have seen him get a share of that and that hasn't happened," he added.
Brighton's 41 points is their best return from their three seasons in the Premier League,
Manager Graham Potter, with no top flight experience had made a number of changes to predecessor Chris Hughton's squad before the campaign and was delighted with their effort.
"It is the first year in the Premier League for myself and a lot of players. To end up with 41 points is good but we want to improve but the Premier League is very tough, every year is tough," he said.