The Clarets looked to be heading to another miserable defeat and a 17th game without a win when they went 2-0 down during the first-half.
But a bonkers seven minutes before the interval turned the game on its head, as Hannibal, Jaidon Anthony and a Jefferson Lerma own goal saw them lead.
The Burnley Express has launched a new WhatsApp channel to bring the latest news, analysis and team & injury updates directly to your phone. Simply click this link to join our Burnley Express WhatsApp channel.
Scott Parker’s side inevitably came under pressure during the second period, but they held firm with a spirited, backs-against-the-wall display to claim a long-overdue three points.
Here’s how Burnley’s players rated:
Your next Burnley FC read: Timeframe placed on Axel Tuanzebe's Burnley return after injury setback
1. Martin Dubravka - 7/10
Pulled off a flying save with virtually the last kick of the game to secure the three points for Burnley. (Photo by Luke Hales/Getty Images) Photo: Luke Hales
2. Kyle Walker - 6/10
Recovered from a poor first half, where he was involved in both of Palace’s goals. But second half he was much better. (Photo by Justin Setterfield/Getty Images) Photo: Justin Setterfield
3. Josh Laurent - 7/10
In many ways sums up this Burnley team. Culpable for the first goal but never gave up and never stopped running. (Photo by Justin Setterfield/Getty Images) Photo: Justin Setterfield
4. Joe Worrall - 8/10
A real mature, experienced display from the defender, constantly marshalling the team on his first start since Bournemouth in December. (Photo by Luke Hales/Getty Images) Photo: Luke Hales