Burnley took a huge stride towards retaining their Premier League existence with their first away win of the season, as goals from Ashley Barnes and Andre Gray moved them above Palace and into 14th place.
Neither side are certain of safety yet, and Palace may face sanctions after James Tarkowski, the Burnley defender, was hit on the head by a cigarette lighter thrown from the crowd as he celebrated the opening goal with his team-mates in the seventh minute.
Tarkowski went down clutching his head after being hit by the lighter, which appeared to come out of the corner of the Holmesdale End, where Palace's self-style 'Ultras' congregate.
The defender received treatment before continuing, and referee Bobby Madley spoke to a steward in order to send reinforcements into the offending section.
Barnes was somewhat fortunate to score, having scuffed his first-time shot from Stephen Ward's low cross. But the ball did not travel far from his feet, and allowed him to move past his marker and drill a second shot beneath the onrushing Wayne Hennessey from close range.
Barnes thought he had scored a second goal 10 minutes later, again bundling the ball in from close range, but Madley changed his mind after initially allowing the goal to stand, realising that Barnes had controlled Michael Keane's flick on with his arm.
Burnley were good value for their lead, nevertheless, and had good chances to increase it. Sam Vokes put one header just over the far post and then had another one well saved by Hennessey before half-time.
Burnley thought they should have had a penalty, too, when George Boyd was pushed over by Jason Puncheon as he waited to head the ball from a corner, but referee Madley thought differently.
Burnley's sense of injustice was nothing compared to Palace's, though, and in particular Wilfried Zaha, who felt he was not getting his fair share of decisions. Zaha was booked early in the second-half for protesting towards one of Madley's assistants, and was lucky to escape a second yellow card as he continued to show dissent towards the referee.
It was understandable. Zaha had been incorrectly given offside as he beat Burnley's backline to run in on goal, and seemed to suffer an inordinate amount of rough treatment from Sean Dyche's uncompromising defenders. He could have had a penalty in the 78th minute when substitute Jon Flanagan clipped his heels inside the penalty area, but again the referee waved play on.
There was frustration, too, when Palace wasted the rare opportunities that came their way as Burnley defended stoically. Luka Milivojevic shot wide from 15 yards when the ball fell to him in a crowded penalty area before half-time, and the Serb had a long shot well saved by Tom Heaton early in the second-half. But the young England goalkeeper made an event better save to keep out a well struck volley from Damien Delaney that seemed destined for the far corner of goal.
But Heaton was well protected for much of the time by his defence, with Tarkowski and Keane outstanding in the centre. Christian Benteke barely had a sniff of goal and was replaced by Loic Remy with 20 minutes remaining.
Dyche made his own change, sending on Andre Gray to replace the tiring Barnes, and the striker responded almost instantly with the goal that killed off Palace, running on to Boyd's pass and drilling the ball past Hennessey in the 84th minute.
“We are staying up,” sang the jubilant away supporters and they may well be right.
Full time: Crystal Palace 0-2 Burnley
The final whistle blows at Selhurst Park.
Average touch positions (full time)
Crystal Palace up against it now - Andre Gray makes it 0-2 to Burnley.
Second half: Crystal Palace 0-1 Burnley
We're back under way at Selhurst Park.
Half time: Crystal Palace 0-1 Burnley
The teams head in at the break at Selhurst Park.
Average touch positions (half time)
Burnley take an early lead and they have Ashley Barnes to thank for it: 0-1.
The visitors have their first shot of the game, in reply to three so far from Crystal Palace.
Kick off: Crystal Palace vs Burnley
The action gets started at Selhurst Park.
Our Roboblogger will bring you every goal from the late game between Crystal Palace and Burnley. In the meantime, here's a match preview.
Sam Allardyce has no qualms with throwing Damien Delaney back into his Crystal Palace side for Saturday's crunch meeting with Burnley.
The Eagles will pass the 40-point mark and all-but secure their Premier League status if they can beat their struggling visitors as Allardyce looks to complete an impressive escape from relegation.
But the former England boss will be without a host of defenders at Selhurst Park as Mamadou Sakho's knee injury against Tottenham adds to the previous losses of Scott Dann and James Tomkins.
That means Delaney, 35, could be given his first start since mid-February having been displaced by Sakho after the Liverpool loanee gained match fitness.
But Allardyce is not worried that Delaney may struggle on his return and has called on the former Republic of Ireland international to show him what he can do.
"It is all about us believing in ourselves and believing in the squad," he said.
"For me, Damien Delaney has been here, seen it and done it for a long period of time at Crystal Palace while they have been in the Premier League.
"He is a very, very adequate step-in for Mama, who got injured; the only problem would be if either him or Martin Kelly got injured in the next few games.
"It is about professionalism isn't it? He is a long-time, seasoned professional and has to draw on his own pride and professional experience by saying 'I am disappointed that the manager hasn't picked me, I think he should have.'
"There is no doubt he will be peeved about the scenario but he is a professional who has kept himself fit and is still playing in the Premier League at his age which is getting rarer and rarer these days.
"I expect him to be 100 per cent professional, as he has always been, he has handled the disappointment extremely well and has always been very good in the dressing room.
"I hope he plays to the capabilities he can play at, there won't be a problem there and if he needs to show me what I was missing I hope he does that as well and says 'There you go, you should have played me sooner'."
Having taken charge at Palace with the club down in 17th, Allardyce could yet lead them to their highest ever Premier League finish.