Burnley spurned a two-goal lead for the second time in four days as Palace came from behind to snatch victory at a wintry Turf Moor.
The Clarets had the perfect start for the second time in a week, racing into a two-goal lead inside 16 minutes through Ben Mee’s first Premier League goal and Danny Ings’ seventh of the season.
But Dwight Gayle halved the deficit before the break before Jason Puncheon levelled matters soon after the break.
And Gayle struck a dramatic late winner to earn the Eagles an unlikely victory that continued their impressive start under new boss Alan Pardew.
Palace, who made two changes, fielded new signing Yaya Sanogo, who joined the club this week from Arsenal.
Burnley, meanwhile, were unchanged for the eighth successive Premier League game, just four shy of Birmingham’s all-time record of 12 set in 2009.
And it took Sean Dyche’s supercharged side just 12 minutes to unlock a defence that had kept three clean sheets in four on the road.
Kieran Trippier swung across a deep corner that evaded everyone and Mee had the simplest of tasks to nod home at the far post.
Amazingly, Burnley soon repeated their whirlwind start at Spurs in midweek with a second!
Trippier’s clearance was chased down the left flank by Scott Arfield, who robbed Joel Ward as the right back tried to let the ball run out of play.
Immediately, the Scot spotted Ings unmarked in the middle and the Clarets striker was coolness personified as he sent Julian Speroni the wrong way with a side-foot finish.
Palace were rocked on their heels, but struck back with their first attempt just before the half hour.
Wilf Zaha’s cross flicked off Trippier into the path of Gayle, who rifled the ball home with a sweet finish.
Trippier, who was involved in all the main incidents, was the Clarets saviour five minutes later when he made a magnificent goal-line clearance from Zaha’s drilled cross, which looked set to be slotted home by Sanogo.
And as the Eagles ended the half the stronger, it took a fine save from Tom Heaton from James McArthur’s long-range effort to retain the slender lead at the break.
Three minutes into the second half the equaliser duly arrived, as Burnley stood off Puncheon as he advanced and found the bottom corner from 25 yards.
Burnley recovered from that hammer blow and gradually got back on the offensive, with Sam Vokes replacing Ashley Barnes as a tight second half entered the final stages.
And as Burnley looked the more likely to win it, Michael Keane saw his goalbound volley from 12 yards, from Shackell’s knock-down, blocked on the line by a retreating McArthur.
Palace thought they had snatched victory themselves as substitute Glenn Murray acrobatically volleyed off the post with five minutes of an absorbing contest remaining.
But they did grab the winner with just three minutes remaining as Gayle stole in at the far post to slide the ball under Heaton.
BURNLEY: Heaton, Trippier, Shackell, Keane, Mee, Arfield, Marney, Jones (Wallace 90) Boyd (Sordell 90), Barnes (Vokes 74), Ings.
Subs: Gilks, Duff, Reid, Kightly.
BOOKED: Shackell 61
PALACE: Speroni, Ward, Dann, Sanog (Murray 79) Zaha (Guedioura 70), Gayle, McArthur, Delaney, Ledley, Kelly (Mariappa 84), Puncheon.
Subs: Hangeland, Campbell, Hennessey, Thomas,
Booked: Dann 17, Sanogo 75, Ward 77
Ref: P Dowd
Att: 17,872 (1,754)