Burnley finally end away hoodoo to all but ensure Premier League safety
A seventh-minute strike from Ashley Barnes and a clincher six minutes from time from substitute Andre Gray claimed Burnley's first away win of the campaign, at the 18th attempt.
And in the process, the Clarets moved onto 39 points, eight clear of Swansea City in 18th place, with four games to go - and a superior goal difference.
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Hide AdSean Dyche sprung a surprise before the game, leaving out Gray as Sam Vokes returned, while Scott Arfield came in for record signing Robbie Brady.
Ashley Westwood replaced the suspended Joey Barton, with James Tarkowski in for the injured Ben Mee.
Burnley were penned in by four successive corners early on by Palace, while Christian Benteke was denied by Tom Heaton after a delightful move down the left.
But two minutes later Barnes struck, as he won the ball high up the pitch, and Vokes and Westwood combined to send Stephen Ward down the left.
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Hide AdHis precise centre picked out Barnes, who fluffed his first effort, but recovered to score at the second attempt.
Burnley's organisation and industry frustrated Palace, and they continued to provide a threat, as Barnes had the ball in the net again, only to see it belatedly ruled out for handball.
Vokes also twice went close, and Burnley were deserving of more than a one-goal lead at the break.
Ward, who went into the game with a knee problem, was replaced by Jon Flanagan just before the break, and the Liverpool defender helped keep Palace at arm's length after the break.
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Hide AdHeaton made a superb save to deny Damien Delaney, but Palace were largely restricted to efforts from distance, and Burnley broke to seal victory six minutes from time as George Boyd sent Gray away, and he finished clinically to claim a famous win for the Clarets.