A day overshadowed by the death of manager Eddie Howe's mother got little better for the Clarets as their continuing inability to win at home saw them stay marooned in mid-table.
With Howe understandably absent, Jason Tindall took charge with youth coach Terry Pashley alongside him in the Burnley dug-out.
But despite the bonus of an early penalty, converted by Jay Rodriguez for his 21st goal of the season, there was to be no change in fortune as Palace levelled in the second half with a spot-kick of their own to make it just one Turf Moor win in the Clarets' last five attempts.
Palace's penalty was not without controversy as Wilfried Zaha went down with seemingly no contact and the England under-21 international was sent off shortly afterwards after apparently kicking out at David Edgar.
But in the absence of the injured Rodriguez, Burnley couldn't take advantage as, despite stopping the rot after a hat-trick of defeats, their campaign stuttered further towards what threatens to be a frustrating finish.
On a difficult afternoon launched by a minute's silence for Howe's mother Annie, the Clarets had made the perfect start with a goal inside the first two minutes.
The Clarets' staff stand in support of absent boss Eddie Howe
There were only 48 seconds on the clock when Martin Paterson was pushed over in the box by Jonathan Parr as the defender tried to make amends for a dreadful back-pass.
After the Norwegian had been booked, Rodriguez stepped up to drill home his ninth goal in 11 games and Burnley went on to dominate the opening exchanges.
Paterson and Danny Ings provided some extra urgency in attack and Ings almost marked his first start in a Burnley shirt with a second goal with 12 minutes gone.
After linking with Rodriguez, the former Bournemouth man weaved his way into the penalty area and only the legs of goalkeeper Julian Speroni denied Ings as he looked to put the cap on a lively start.
Jay Rodriguez fires the Clarets in front from the spot
Palace, unbeaten in seven games, were reliant on trying to counter on the break as they played into a strong wind and the lively Zaha teed up Glenn Murray for an angled shot which was easily saved by Lee Grant.
The Clarets continued to pose the greater threat, Kieran Trippier striding forward from right-back to thread a low shot just wide and then pulling the ball back for Rodriguez to fire over the top from the edge of the penalty area.
Danny Ings is denied by Julian Speroni
But Murray then gave them a further reminder of the slender nature of their lead eight minutes before the break when he met a Darren Ambrose cross with a firm header which Grant palmed away from the top corner in spectacular style.
Grant was also forced to save from Chris Martin and Paddy McCarthy from the corner that followed as Burnley loosened their grip.
And with top scorer Rodriguez not appearing at the start of the second half, the Clarets still had work to do secure only a second home win since the turn of the year.
In an incresasingly scrappy game there was a half-chance for Paterson with a shot on the turn from substitute Josh McQuoid's low cross.
But Palace had begun to knock on the door and with just less than half an hour to go they levelled with the second spot-kick of the afternoon.
Dean Marney feels the force of a foul from Stuart O'Keefe
Zaha had just been taken out by Michael Duff as he raced goalwards and when the winger jinked his way into the box moments later he went down after brushing past Trippier.
There didn't look to be much in it but referee Dean Whitestone saw sufficient to award a penalty which Ambrose drove home low to Grant's right.
The Clarets were less than impressed with Zaha's lack of balance and there may have been some 'left-overs' ten minutes later when Zaha was involved in an off-the-ball clash with Edgar and duly saw red following the intervention of an assistant referee as tempers flared.
Martin Paterson tries to find a way through
That left Palace, who had just survived a close call when Speroni made a fine save from Trippier's free-kick, to face the final 20 minutes with ten men .
Tindall sent on Charlie Austin and belatedly Junior Stanislas to try and make them pay but despite the persistence of Dean Marney and Ben Mee getting forward from left-back there was no spark to seriously threaten a winner.
Burnley: Grant, Trippier, Mee, Duff, Edgar, Marney, McCann, Wallace (Austin 75), Rodriguez (McQuoid ht), Paterson (Stanislas 89), Ings. Subs: Stanislas, Bartley, Jensen.
Booked: Duff 58, Marney 62
Crystal Palace: Speroni, Clyne, Parr, McCarthy, Gardner, Ambrose, Jedinik, Zaha, Murray, O'Keefe, Martin (Moxey 73). Subs: Garvan, Easter, McShane, Price.
Booked: Parr 1, O'Keefe 68. Sent off: Zaha 72
Referee: Dean Whitestone.
Palace go down to ten men as Wilfried Zaha sees red