A dismal match offered little to excite the punters, although the final quarter livened up.
Palace had the edge in terms of possession but lacked firepower. Andy Johnson went close from Julian Gray's cross in the early stages and then on 30 minutes Gray fired a good chance over the bar after good work on the left from Johnson.
Burnley sitting just above the drop zone and with Palace not that far above indeed looked two sides that will struggle for the rest of the season.
Robbie Blake was playing well for Burnley causing Palace defence concern on a number of occasions, but he had little support.
On the hour it was from Blake's free-kick that Mark McGregor's header forced Thomas Myhre to make his first save of the afternoon.
Burnley were enjoying their best spell so far with Myhre called up to make stops from Blake, Glenn Little and Luke Chadwick to cheer up their 772 travelling fans.
Substitute Dougie Freedman missed a good chance, after taking too long to pick his spot, while Ben Watson shot recklessly over as Palace replied at the other end.
The final ten minutes or so saw relentless pressure from the Eagles as Freedman, Gray and Danny Granville could all have scored in a frantic finish, but it came all too late as time ran out and Burnley got a point that they just about deserved.