Ashley Barnes struck another dramatic Turf Moor winner to propel the Clarets into the top 10 of the Premier League.
For the second home game running, Sean Dyche’s never-say-die side pounced late on to secure a fourth home win of the campaign and go into the international break in a superb position in the table.
As two years ago in the corresponding fixture, the Clarets had led 2-0 thanks to early goals from top scorer Sam Vokes and Johann Berg Gudmundsson.
Again Crystal Palace came back with second-half goals from substitute Connor Wickham and a Christian Benteke penalty to level and set up a nerve-wracking finish.
But this time Burnley refused to go under in the face of mounting pressure and grabbed an injury-time winner when super-sub Barnes came off the bench to ram home a memorable first goal since February, 2015 and cap another character-filled performance from his side.
Boss Dyche brought back Steven Defour following the midfielder’s recovery from injury, with the Belgium international replacing Andre Gray as the Clarets went back to the formation that had seen them beat Everton in their previous home game.
That left Vokes as the lone frontman but Burnley’s attacking threat was far from negated and within 90 seconds they were 1-0 up thanks to a breath-taking start.
Jeff Hendrick was the man deployed to provide the support for Vokes and he launched the counter-attack which ended with Vokes’ fourth goal of the season.
Hendrick’s initial attempt to release Gudmundsson was blocked but the impeccable Defour kept the move going with a ball to Matt Lowton who played in Gudmundsson.
The Icelander was forced wide but returned the favour with a cross for Lowton, whose shot was parried by Steve Mandanda into the path of Vokes, who beat defender Scott Dann on the line to force the ball home from a couple of yards out.
The goal extended Palace’s record of conceding in every league game this season but the Eagles are not short of power at the other end and could have been level with 14 minutes gone had goalkeeper Tom Heaton not again showed his class.
In front of watching acting England boss Gareth Southgate – also checking on Burnley defender Michael Keane before naming his latest squad – Heaton spread himself superbly to block a far-post volley from Wilfried Zaha.
And the value of that save was underlined when the Clarets went 2-0 up within 60 seconds.
This time Vokes was the provider with a through-ball to Gudmundsson who ran clear and hit a left-foot shot with such power that France international Mandanda was unable to get enough of a hand to keep the ball out of the net and deny the winger his first Burnley goal.
The Clarets had one further chance to extend their lead before the break with a Hendrick shot that was blocked but - unlike two years ago when Palace hit back early on the way to a 3-2 win - Dyche’s men protected their two-goal advantage until half-time as the dangerous Andros Townsend fired inches wide from an excellent chance and Benteke shot straight at Heaton.
Despite those scares, the Clarets always looked to be just one more goal away from a more comfortable victory and they twice nearly got it within the opening minutes of the second half.
Again Vokes was the man, firstly dragging a shot just wide on the turn and then going it alone from Scott Arfield’s fine ball over the top before being thwarted by Mandanda’s smart double save at the near post.
The in-form Vokes was a constant handful for the Palace defence, stabbing another difficult chance wide from Defour’s pull-back.
But with Palace boss Alan Pardew deciding a change was needed to try and get his side back into the game, he made a double swap 12 minutes into the second half which paid immediate dividends as Palace launched their fightback.
Wickham had only been on the pitch for a minute when he met Zaha’s excellent low cross with a superb first-time finish into the top corner.
And with the momentum going Palace’s way it was increasingly a backs-to-the-wall effort from the Clarets.
But when the equalising goal did come, it followed a Clarets corner as Palace broke away and won a penalty when a cross from Townsend was blocked by the arm of Lowton, allowing Benteke to stroke home the leveller from the spot.
A point at that stage might have felt like scant reward for the Clarets, given their earlier efforts, but, thanks to Barnes, one became three in another remarkable finish.
The striker was brought on to provide fresh legs as an attacking option in the closing stages and the plan worked to perfection as he launched and finished off the decisive move.
His initial pass denied Gudmundsson a shooting chance but the wideman capped a superb performance by squaring the ball perfectly for Barnes to thunder a shot into the roof of the net in the fourth minute of added time to put the memories of his injury-hit run firmly behind him.
Palace still had long enough to hit a post through Townsend but Burnley would not be denied as once again they showed Turf Moor is not a place to leave early.
Burnley: Heaton, Lowton, Keane, Mee, Flanagan, Gudmundsson, Marney, Hendrick (Barnes 86), Defour (Tarkowski 74), Arfield (Boyd 65), Vokes. Substitutes: Robinson, Kightly, Gray, Bamford, Barnes.
Crystal Palace: Mandanda, Kelly (Fryers 59), Dann, Delaney, Ward, Cabaye, McArthur (Ledley), Puncheon (Wickham 59), Townsend, Zaha, Benteke. Substitutes: Hennessey, Flamini, Tomkins, Lee Chung-Yong, Ledley.