The Clarets’ inability to hold onto a lead again cost them dear as a second-half collapse allowed Palace to continue their surge up the table.
After carelessly letting home points slip through their grasp in their last two games, Burnley took another backward step as they saw a two-goal lead evaporate in the London sunshine.
When Chris McCann and Martin Paterson struck inside the first half-hour the Eagles should have been looking at the end of their six-match unbeaten run.
But a goal back from Wilfried Zaha just before the break laid the platform for a comeback as Zaha, again, Damian Delaney and Glenn Murray struck in the space of 23 minutes.
Charlie Austin’s 11th goal in six games offered a late glimmer of hope but even with the country’s leading scorer in their ranks the Clarets don’t currently have what it takes to turn winning positions into the hard currency of points as they head for the international break in the wrong half of the table.
The return from injury of Jason Shackell and McCann and a starting chance for Marvin Bartley in midfield meant three changes for the Clarets’ following their mid-week draw at home to Sheffield Wednesday.
And manager Eddie Howe also opted to change his formation with Dean Marney asked to shield the back four and Paterson filling in on the right-hand side of midfield as Charlie Austin foraged alone up front.
As a result the Clarets made themselves hard to pass with a scrappy opening suiting their needs as Palace gained no momentum in their quest to extend a three-match winning run.
Any early threat the Eagles did muster came from long range as dangerman Zaha forced Lee Grant into a save and Yannick Bolasie skidded an effort just wide.
And just when the home side did look as though they might be about to exert some control the Clarets went in front.
Darcy Blake was guilty of a poor defensive header as he attempted to clear a cross from Kieran Trippier and when Junior Stanislas kept the ball alive he had Palace on the back foot.
A curling shot from Stanislas was pushed onto a post by Julian Speroni but McCann timed his follow-up perfectly to meet the rebound on the volley eight yards out and fire the ball past a covering defender on the line.
And if that was good things then got even better for the Clarets with a second goal in the space of three minutes as the half-hour mark approached.
Paterson had admitted before the game that he needed a goal, having not scored since the opening day of the season.
And he got his wish with a fantastic finish, accepting a pass from Bartley near the corner of the penalty area to lift a perfectly angled lob over Speroni and into the far corner of the net before celebrating with fitness coach Jon Dalzell.
Having looked solid at the back the Clarets would have loved to have taken that lead into the break but four minutes before half-time Palace gave themselves a lifeline.
The pace of Zaha had been well contained but when Glenn Murray slid a pass in behind the Burnley back four the winger took flight and after getting away from Trippier beat Grant to claim his third goal in two games.
Burnley responded well with Austin and Paterson opening up the Palace defence for McCann to unleash a goalbound shot which cannoned into a defender.
But with the advantage halved Palace knew they were back in the hunt and seven minutes into the second half they made it 2-2 thanks again to Zaha and some terrible defending.
Within seconds of attacking at one end, the Clarets were suddenly hopelessly outmanned at the other as Palace broke and released Zaha via a pass from Andre Moritz.
With no defender to beat, the winger cut in onto his right foot and although finally faced by a white shirt he was able to pick his spot and roll a shot past the helpless Grant.
There was an immediate inquest in the Clarets’ rank as their early resoluteness had again deserted them at a critical moment and for once Austin was unable to bail his side out as he failed to take a half-chance from Paterson’s pull-back.
And with the impetus firmly with Palace they went ahead for the first time with 25 minutes to go as the Clarets again failed to clear the ball and Delaney pounced to ram home a shot from on the penalty spot.
With their confidence seemingly rocking Burnley had no answer to the rampant Londoners who then added a fourth ten minutes later as Murray coolly steered a low cross inside the far post.
That was his seventh goal in as many games but even the in-form Murray can’t hold a candle to Austin who replied with his 15th goal of the season.
Again the striker finished with unerring accuracy with a shot on the turn from just inside the penalty area with nine minutes to go.
Burnley then poured forward in search of an unlikely point saver and Ross Wallace claimed a penalty after a cross was driven against a defender's arm.
But despite five minutes of added time, the Clarets couldn’t create the one more chance they needed to repair the earlier damage.
Burnley: Grant, Trippier, Mee, Edgar, Shackell, Marney, McCann (Stewart 71), Bartley, Austin. Paterson (Vokes 71), Stanislas (Wallace 85). Subs: Mills, Stock, Long, Jensen.
Booked: Edgar 57, Trippier 62
Crystal Palace: Speroni, Blake, Delaney, Ramage, Moxey, Jedinak, Bolasie (Williams 65 (Parr)), Dikgacoi, Moritz (Garvan 83), Murray, Zaha. Subs: Ward, Parr, Goodwille, Garvan, Wilbraham, Price.
Attendance: 20,863 ( Burnley 779)