Dougie Freedman was the hero, grabbing a hat-trick as Palace pulled off a sensational win after finishing with just nine men.
The Scottish striker was outstanding but Burnley's defending left a lot to be desired in a quite extraordinary opening day clash.
A Freedman penalty in the third minute, after he himself had been felled by Lee Roche, put Palace on their way. Burnley responded with two goals themselves to turn the game on its head within quarter of an hour.
Robbie Blake drew them level with a great strike from a free kick and Roche went even better with a ferocious shot into the top corner while Palace also suffered the disappointment of losing Wayne Routledge, sent off for a foul on Lee Chadwick.
Burnley seemed to be in pole position but their defending was also suspect and a mix-up between Roche and goalkeeper Brian Jensen enabled Freedman to equalise in the 32nd minute.
Burnley tried to get their attacking game together and both Blake and Alan Moore were unlucky with goal-bound shots that were brilliantly saved by Palace keeper Matt Clarke.
Clarke's heroics seemed to take their toll on Burnley who then slid behind after a poor piece of goalkeeper by new boy Jensen.
He failed to deal properly with a cross from Andy Johnson that left Freedman with the easiest of close-range headers to complete his hat-trick.
Burnley boss Stan Ternent pulled no punches afterwards, hinting that he may be in the market for some new defenders.
"We were OK going forward but conceded three very poor goals, but there was nothing that happened out there that I don't know already.
“We worked hard in pre-season and hoped to start with a win, but it just didn't happen for us.
“It was self-inflicted and we have to do better." Hero Freedman said: "I think that's the tenth hat-trick of my career and I have always had a personal goal to get one on the first day of the season. To do it is fantastic."