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.
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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:
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5. Maxime Esteve - 7/10
Allowed Strand Larsen to get ahead of him for Palace’s second, but was otherwise rock solid. Produced an important block to deny Strand Larsen his hat-trick. (Photo by Justin Setterfield/Getty Images) Photo: Justin Setterfield
6. Bashir Humphreys - 7/10
Playing in an unfamiliar role at left wing-back, but carried it out well. His header forced the own goal for Burnley’s winner. (Photo by Justin Setterfield/Getty Images) Photo: Justin Setterfield
7. Hannibal - 9/10
Arguably his best display in a Burnley shirt, and not just because of his sweet strike. Ran the show at times and kept his cool even when targeted by Palace’s players. (Photo by Luke Hales/Getty Images) Photo: Luke Hales
8. Lesley Ugochukwu - 7/10
A really good shift. Asked to play a more disciplined role in midfield and he stuck to his task well, using his attributes to good effect. (Photo by Luke Hales/Getty Images) Photo: Luke Hales