The Clarets finished three points adrift of Leeds United, who beat nine-man Brentford with the last kick of the game to preserve their status in the top flight.
Burnley were downed by a Callum Wilson double; the first from the spot after Nathan Collins’ needless handball from a Kieran Trippier corner.
The striker then doubled the Magpies’ advantage when guiding Allan Saint-Maximin’s cross beyond Nick Pope from close range.
Leading scorer Maxwel Cornet thumped the ball past Martin Dubravka on the volley to give Mike Jackson’s men a lifeline.
They pressed for an equaliser, but substitute Wout Weghorst poked the ball wide from close range, Jack Cork’s header was cleared off the line and a corner header was saved by Dubravka.
Here are the player ratings.
The striker then doubled the Magpies’ advantage when guiding Allan Saint-Maximin’s cross beyond Nick Pope from close range.
5. James Tarkowski 5
Gave everything to aid Burnley's cause, but his time at the club ultimately ended in the worst possible way. Enjoyed a competitive tussle with Wilson, for which he received a booking in one instance, and limited the away side's openings in and around the penalty area. Clearly cut up by the final result. Photo: Richard Heathcote
6. Kevin Long 4.5
Didn't do a great deal wrong, though the back three seemed to be standing on each other's toes far too often. Moved across to cover the full back areas when necessary, but nowhere in sight as Wilson doubled Newcastle's lead. Photo: Alex Livesey
7. Josh Brownhill 4.5
A disjointed display from the midfielder, who never really settled into the game. Busy, determined, and broke up play, but couldn't pick a pass, which prevented the home side from gathering any momentum. Photo: Gareth Copley
8. Jack Cork 4.5
Attempted to get close to Bruno Guimaraes and pressurise the Brazilian, but wasn't really a match for the ex-Lyon midfielder. Wasteful on the ball in the first half, but his influence grew as Burnley sought a route back into the game. Effort from Cornet's lay-off was cleared off the line at 2-1. Photo: Jan Kruger