Burnley scored three goals in the last 10 minutes as they fought back to win.
Palace led 2-0 after Shefki Kuqi took advantage of a defensive mix-up to find the net and Paul Ifill's drive was turned in by defender Clarke Carlisle.
Carlisle pulled one back with a header before Clint Hill was harshly penalised for a push on Steven Thompson and Graham Alexander scored from the spot.
Thompson put Burnley ahead with a fierce strike on 88 minutes and Jay Rodriguez slotted in the fourth.
Burnley boss Owen Coyle: "It's game 49 of this season and it would have been really easy for the players to hide themselves away at 2-0 down.
"But they wouldn't roll over, we kept going right to the end.
"I felt so aggrieved to be 2-0 down, but I said at half-time I'd be disappointed if we didn't win it, let alone get a draw."
Crystal Palace boss Neil Warnock: "After their penalty went in there was only going to be one team who won it. It knocked the stuffing out of us and we've got to show more.
"We're not anywhere near, we know we need surgery in the summer, but tonight answered a few questions for me.
"But it's all good for me but it's disappointing for us at the moment."
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