A Dwight Gayle goal three minutes from time completed an extraordinary comeback for Palace who came from two goals down to win their third consecutive game at Burnley.
Alan Pardew’s side fell 2-0 down just 16 minutes into the game thanks to goals from Ben Mee and Danny Ings, but Gayle struck on 27 minutes to give his side hope during the break.
Jason Puncheon pulled Palace level three minutes after the restart before Gayle struck at the death to complete the turnaround and win back-to-back league games under Pardew.
The game was just 12 minutes old when the hosts found a way past Julian Speroni. After Ings had seen a shot blocked and deflected wide for a corner, Kieran Trippier whipped a great delivery across the area and Mee snuck in at the back post to head the ball in.
And it got even worse for Palace when they conceded a controversial second four minutes later. Amongst a heavy hailstorm a long Trippier clearance saw Joel Ward attempt to shield the ball out of play under pressure from Scott Arfield, however the winger nipped in to win the ball and play in Ings who had all the time in the world to slot the ball past Speroni.
Looking down and out, Palace needed a quick response to end the constant pressure from Sean Dyche’s side and got it on 27 minutes with their first meaningful attack of the game. Wilfried Zaha burst down the right flank past Arfield and Mee and put a dangerous cross into the box which James McArthur deflected onto Trippier and it fell to Gayle, who had time to control the ball and fire it into the net to get his side back into the game.
That seemed to wake Palace out of their slumber, with Zaha much more of a threat after switching from the left flank to the right. It was down that channel again that saw another opportunity for the visitors when Zaha laid the ball off to Ward but the full-back’s attempted shot from the edge of the box was well over.
Pardew’s side finished the half the strongest and McArthur saw a low skidding effort saved by Heaton before in stoppage time debutant Yaya Sanogo had a header from a corner flicked wide by a defender as the Eagles pressed for an equaliser.
And they got it a couple of minutes after the restart. Puncheon picked the ball up 30 yards from goal and ran at the Clarets defence before drilling a low effort from just outside the area into the bottom corner out of Heaton’s reach to complete the comeback.
Having pulled level Palace continued to enjoy superiority in the game but could only put down a weak attempt from McArthur as an attempt which he screwed wide, however the Scot was in the perfect place to save his side when he cleared a half-volley from Michael Keane off his own line 12 minutes from time, which would ultimately prove to be crucial.
Only the woodwork denied Pardew’s side from taking the lead on 83 minutes when an Adlene Guedioura corner was headed out of the area but then lofted into the path of fellow substitute Glenn Murray, who scooped the ball goalwards on the volley but saw it beat Heaton but not the upright.
But with three minutes to go Palace incredibly, but deservedly, edged ahead. Puncheon drifted a fine ball into the box for Gayle, who allowed his first touch to get away from him before sliding the ball past Heaton into the bottom corner to send the travelling Eagles fans into raptures, and the visitors held on to claim a huge three points.
Burnley: Heaton, Trippier, Keane, Shackell, Mee, Boyd (Sordell 90), Marney, Jones (Wallace 90), Arfield, Ings, Barnes (Vokes 73). Subs not used: Gilks, Duff, Reid, Kightly.
Palace: Speroni, Ward, Dann, Delaney, Kelly (Mariappa 83), Puncheon, McArthur, Ledley, Zaha (Guedioura 70), Sanogo (Murray 78), Gayle. Subs not used: Hennessey, Hangeland, Thomas, Campbell.