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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9. Marcus Edwards - 6/10
Made a nuisance of himself and teed up Hannibal for his sweet strike,, but his final ball was sloppy, often resulting in Palace counters. (Photo by Dan Istitene/Getty Images) Photo: Dan Istitene
10. Jaidon Anthony - 8/10
Took his goal really well, giving the keeper the eyes and picking out the bottom corner. Also provided the corner for Burnley’s third. (Photo by Justin Setterfield/Getty Images) Photo: Justin Setterfield
11. Zian Flemming - 6/10
Struggled to hold the ball up at times but put in a great shift for the team. Missed a gilt-edged chance in the first-half when he was leaning back. (Photo by Molly Darlington/Getty Images) Photo: Molly Darlington
12. SUB: Jacob Bruun Larsen - 6/10
For Edwards, 72 Had a golden chance to put the game to bed for good when he volleyed just wide on his left foot. (Photo by Steve Bardens/Getty Images) Photo: Steve Bardens