Steve Bruce’s side came from behind at Turf Moor to end their seven-game winless run.
Matej Vydra put Burnley ahead in the first half, but Jacob Murphy equalised and Allan Saint-Maximin grabbed the priceless winner.
Fourth bottom Newcastle are now six points clear of the relegation zone and hold a game in hand on third bottom Fulham.
Burnley are seven points above the bottom three, but aren’t certain of survival after just one win from their last eight matches.
The hosts took the lead with 18 minutes gone as Ashley Westwood pounced on a poor header from Newcastle defender Ciaran Clark.
Westwood played in Chris Wood and he pulled the ball back from the touchline for Vydra to net from close-range.
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But French winger Saint-Maximin turned the game after coming on as a 57th minute substitute.
Saint-Maximin surged down the right flank and drew three defenders towards him before pulling the ball back for Murphy to equalise in the 59th minute.
Five minutes later, Saint-Maximin produced a brilliant individual effort as he ran at the Burnley defence before driving his low shot past Bailey Peacock-Farrell.