Burnley continued to press but Palace held firm, Henderson particularly impressive in making a brave low dive to turn away Marcus Edwards’ fizzed cross.
The hosts threw on additional attackers in the game’s closing stages – and did have one late close-range free-kick from Edwards, which thankfully hit the wall, as well as a looping header from Armando Broja which needed clearing off the line by Chris Richards.
But Palace hung on for a hard-fought, but important, away win, one which lifted them us up to fifth in the Premier League table.
Burnley: Dubravka (GK), Walker, Ekdal, Esteve, Hartman, Cullen (Broja, 81), Florentino (Ugochukwu, 71), Tchaouna (Bruun Larsen, HT), Anthony (Edwards, 58), Foster, Flemming (Mejbri, 58).
Subs: Weiss (GK), Worrall, Pires, Laurent.
Palace: Henderson (GK), Richards, Lacroix, Guéhi, Muñoz, Lerma, Wharton (Hughes, 75), Mitchell, Pino (Devenny, 64), Kamada (Canvot, 89), Mateta (Nketiah, 64).
Subs: Benítez (GK), Matthews (GK), Clyne, Uche, Esse.
As It Happened