The win at Turf Moor keeps Burnley firmly in the play-off picture ahead of another home clash this weekend, against Forest.
"I know the effort and desire they've got for the football club to win matches, and it was very evident against Palace," boss Owen Coyle told the Burnley Express.
"I think the whole top half of the Championship would have been rubbing their hands after half an hour when we were 2-0 down.
"But again the lads have shown real courage and bravery, to go with the physical fitness and mental strength, to see it through. "