Goals from Leon Cort and James Scowcroft gave Palace a point but it could have been three as Burnley goalkeeper Brian Jensen made some outstanding saves in the final 10 minutes.
After falling behind twice Palace fought back and if it was not for a lacklustre first-half performance the Eagles probably would have been going away with all three points.
As expected Peter Taylor made nine changes to the side that lost 2-1 to Notts County in the Carling Cup during midweek. Dougie Freedman and Mark Hudson were the only two survivors from that game while Matt Lawrence, Scott Flinders, Marco Reich and Michael Hughes were all on the bench.
Both sides seemed to be cancelling each other out in the early minutes of the game. Although in the sixth minute Danny Granville had to be alert as he hooked away Steve Jones' deflected cross from the left. A few minutes later and Mike Duff headed over from an Alan Mahon free-kick and if the ball over had been a few feet lower then he would have had a great chance to open the scoring for the Clarets.
After 15 minutes Palace created their first chance of the match as Granville's deep cross found James Scowcroft at the far post. The tall striker headed the ball back for Freedman who's first time volley flew just wide of Brian Jensen's far post.
It was Burnley though, who looked the more dangerous side and in the space of two minutes they had two good chances to score. Mahon's long range shot was deflected up into the air, but Andy Gray could only produce a soft header and Gabor Kiraly was able to scramble the ball wide. Then a few seconds later Gray tried a long range drive which flew well wide, although he should have done much better with the space he was allowed by the Palace defence.
Palace had been given a few warning signs and in the 23rd minute Burnley took a deserved lead. Jones found space on the left and his pull-back was tucked into the corner of the goal by Republic of Ireland midfielder Mahon from just inside the penalty area.
Palace huffed and puffed but they could not string of passes together. However, in the 35th minute Scowcroft came close to equalising for the Eagles with a 20 yard thunderbolt that hit the inside of the post with the ball agonisingly bouncing to safety.
As half-time approached Palace put the Burnley defence under intense pressure as they won a number of corners and free-kicks around the box. But the Clarets continued to get bodies in the way and, Burnley striker Kyle Lafferty even took a Mark Kennedy volley flush to the face, such was the Clarets' determination.
Burnley were forced into a change at half-time with defender John McGreal being replaced by Stephen Foster and the Clarets found themselves under pressure immediately from a rejuvenated Palace side.
Three minutes into the second-half and Palace were level. Kennedy's free-kick from the right found Leon Cort at the back post and his looping header flew past Jensen in the Burnley goal. It was the big centre-back's second goal of the season and it provided a much needed boost to the Palace side.
Unfortunately the scores stayed level for three minutes as Burnley retook the lead through Lafferty. Jones' ball from the left flicked off a Palace defender and the Northern Ireland international beat Granville at the far post to poke the ball past Kiraly.
After a brief lull Palace fought back as Freedman looped a shot over after Jensen failed to collect a Fletcher cross from the left in the 58th minute. The cross proved to Fletcher's final act of the game as he was replaced a few moments later by Michael Hughes, now fully fit after his wrist injury.
For all their possession Palace could not create any clearcut chances and they were limited to long range strikes that failed to trouble Jensen. That was until the 75th minute anyway when Jobi McAnuff's cross from the left met the head of Scowcroft, who made no mistake from six yards out.
There was heart in mouth moment for Palace fans a few minutes later though, as for they nearly conceded again just after getting back into the game. Mahon's beautifully flighted free-kick flew right across goal and substitute Foster thumped a header against the underside of the crossbar. Burnley appealed for the goal but referee Lee Probert waved their protests away.
For the final 10 minutes Palace threw everything at Burnley but goalkeeper Jensen was on top form. First he denied McAnuff, what would have been a goal of the season contender, after the winger had skipped past three defenders before cutting inside, and unleashing a shot. Then with only three minutes left Jensen again pulled off a world class save, this time from a Mark Hudson header following Kennedy's corner.
Even in stoppage time Jensen continued to perform miracles, producing perhaps his best save of the match in the final minute of injury time. Kennedy's piledriver looked certain to nestle in the top corner of the Holmesdale Road goal but Jensen dived and twisted his body to get his right hand to the ball and tip it over the bar.
Palace: Kiraly; Butterfield, Hudson, Cort, Granville; Soares, Fletcher (c) (Hughes 59), Kennedy, McAnuff; Freedman (Morrison 77), Scowcroft.
Subs: Flinders, Lawrence, Reich.
Goalscorers: Cort (48), Scowcroft (75).
Burnley: Jensen; Sinclair (c), Duff, McGreal (Foster h-t), Harley; Jones, Hyde, Mahon, J O'Connor (Branch 73); Gray, Lafferty (Noel-Williams 73).
Subs: Elliott, Spicer.
Goalscorers: Mahon (23), Lafferty (51).
