JUNIOR Stanislas' third goal of the season was enough to secure back-to-back league wins for the Clarets.
The winger earned only his second start under Sean Dyche, after announcing his recovery from a hamstring injury with two goals in a midweek friendly with Everton.
Burnley looked like they might not have anything to show for dominating third-placed Crystal Palace.
But Stanislas bent an excellent right foot shot from the edge of the box around Julian Speroni in the 81st minute.
Sam Vokes, who had missed a number of earlier chances, was then stopped from doubling the lead by Speroni, and had a follow-up header deflected wide.
Burnley had limited Palace for long periods but found themselves with defending to do at the death as the visitors desperately pushed for an equaliser.
The Clarets held firm, though, to maintain a 100 per cent start to 2013 in the Championship.