Callum Wilson also scored for Newcastle in their first win of the season - a 1-0 victory over Burnley in December
Burnley were relegated from the Premier League on a dramatic final day as a home loss to Newcastle United condemned them to the Championship.
At the start of the day, Burnley were above Leeds on goal difference, but Jesse Marsch's side won 2-1 at Brentford to end the Clarets' six-year spell in the top flight.
Callum Wilson scored twice for Newcastle through a calm penalty after Nathan Collins' needless handball, then from Allan Saint-Maximin's cross.
Burnley, who sacked long-serving manager Sean Dyche with eight games to go, got a goal back as Maxwel Cornet blasted in a volley after his first effort had been parried by Martin Dubravka.
When Leeds' advantage was cancelled out at Brentford there was fresh hope among the home fans, but their team could not force an equaliser - and Leeds' injury-time winner meant even that would not have been enough.
A miserable end to a tough campaign for Burnley
Some Burnley fans were calling this the team's most important match since 1987, when they beat Leyton Orient to avoid dropping out of the old Fourth Division and out of the Football League altogether.
And to lose such a match - particularly at home - was a terrible way for their time in the elite to come to an end.
At full-time, some players fell to their knees before joining interim boss Mike Jackson in applauding the fans.
But the brutal truth is Burnley have not been good enough this season. They have been in the bottom three most of the campaign having failed to win any of their opening nine games, with an 11-match winless run following soon after.
To the surprise of the club's fans, pundits and players, Burnley owner and chairman Alan Pace sacked Dyche in April, with under-23s coach Jackson given the task of keeping them in the Premier League.
He had taken 11 points from his opening seven games, but his team produced a tame first half at Turf Moor as they only registered one shot on target.
When Wilson scored his second, it looked all over before Burnley finally gave their fans hope of an incredible fightback.
With Leeds still drawing, Burnley produced their best football of the afternoon as Jack Cork had an effort cleared off the line by Matt Targett, before Cornet twice had efforts at goal and Ashley Barnes had a shot saved.
But Burnley ended the season with the second fewest total of goals, with only bottom-of-the-league Norwich scoring fewer, and their failure to finish off their late chances saw them exit the Premier League.
More to follow.
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Player of the match
WilsonCallum Wilson
with an average of 8.61
- BurnleyBurnleyBurnleyNewcastleNewcastle UnitedNewcastle United
BurnleyAvgSquad number1Player namePopeAverage rating
5.60
Squad number20Player nameCornetAverage rating
5.29
Squad number14Player nameRobertsAverage rating
5.19
Squad number17Player nameLennonAverage rating
5.13
Squad number5Player nameTarkowskiAverage rating
4.97
Squad number9Player nameWeghorstAverage rating
4.90
Squad number28Player nameLongAverage rating
4.80
Squad number22Player nameCollinsAverage rating
4.79
Squad number8Player nameBrownhillAverage rating
4.72
Squad number10Player nameBarnesAverage rating
4.69
Squad number3Player nameTaylorAverage rating
4.66
Squad number4Player nameCorkAverage rating
4.65
Squad number11Player nameMcNeilAverage rating
4.63
Newcastle UnitedAvgSquad number9Player nameWilsonAverage rating
8.61
Squad number39Player nameBruno GuimarãesAverage rating
8.37
Squad number15Player nameTrippierAverage rating
8.30
Squad number33Player nameBurnAverage rating
8.17
Squad number10Player nameSaint-MaximinAverage rating
8.15
Squad number13Player nameTargettAverage rating
8.07
Squad number1Player nameDúbravkaAverage rating
7.83
Squad number7Player nameJoelintonAverage rating
7.81
Squad number24Player nameAlmirónAverage rating
7.75
Squad number6Player nameLascellesAverage rating
7.60
Squad number36Player nameS LongstaffAverage rating
7.59
Squad number20Player nameWoodAverage rating
7.44
Squad number11Player nameRitchieAverage rating
7.39
Squad number23Player nameMurphyAverage rating
7.25
- Line-upsMatch StatsLive Text
Line-upsBurnley
Formation 5-3-2
1Pope14Roberts22Collins28Long5Tarkowski3Taylor11McNeil8Brownhill4Cork10Barnes20Cornet
- 1Pope14RobertsSubstituted forWeghorstat 45'minutes22Collins28Long5TarkowskiBooked at 65mins3Taylor11McNeil8BrownhillSubstituted forLennonat 73'minutes4Cork10Barnes20Cornet
Substitutes
- 9Weghorst13Hennessey16Stephens17Lennon26Bardsley37Thomas39Dodgson44Costelloe49McGlynn
Newcastle
Formation 4-3-3
1Dúbravka15Trippier6Lascelles33Burn13Targett36S Longstaff39Guimarães Rodriguez Moura7Joelinton24Almirón9Wilson10Saint-Maximin
- 1Dúbravka15Trippier6Lascelles33Burn13Targett36S Longstaff39Guimarães Rodriguez Moura7JoelintonSubstituted forMurphyat 11'minutes24AlmirónSubstituted forRitchieat 89'minutes9Wilson10Saint-MaximinSubstituted forWoodat 72'minutes
Substitutes
- 3Dummett5Schär11Ritchie17Krafth18Fernández20Wood23Murphy26Darlow34Gayle
Referee:Craig PawsonMatch StatsHome TeamBurnleyAway TeamNewcastlePossessionHome51%Away49%ShotsHome12Away8Shots on TargetHome5Away6CornersHome8Away2FoulsHome8Away9Live TextPost update
Match ends, Burnley 1, Newcastle United 2.
90'+5'Full Time
Second Half ends, Burnley 1, Newcastle United 2.
90'+3'Post update
Offside, Burnley. Ashley Barnes tries a through ball, but Maxwel Cornet is caught offside.
90'Post update
Attempt missed. Callum Wilson (Newcastle United) left footed shot from outside the box is high and wide to the left. Assisted by Martin Dúbravka.
89'Substitution
Substitution, Newcastle United. Matt Ritchie replaces Miguel Almirón.
89'Post update
James Tarkowski (Burnley) wins a free kick in the defensive half.
89'Post update
Foul by Chris Wood (Newcastle United).
88'Post update
Attempt saved. Maxwel Cornet (Burnley) header from the centre of the box is saved in the centre of the goal. Assisted by Charlie Taylor with a cross.
85'Post update
Attempt saved. Callum Wilson (Newcastle United) right footed shot from outside the box is saved in the top centre of the goal.
84'Post update
Offside, Burnley. Dwight McNeil tries a through ball, but Kevin Long is caught offside.
83'Post update
Corner, Burnley. Conceded by Jamaal Lascelles.
83'Post update
Corner, Burnley. Conceded by Jamaal Lascelles.
83'Post update
Corner, Burnley. Conceded by Bruno Guimarães.
83'Post update
Attempt blocked. Dwight McNeil (Burnley) left footed shot from a difficult angle and long range on the right is blocked.
81'Post update
Foul by Matt Targett (Newcastle United).
81'Post update
Jack Cork (Burnley) wins a free kick on the right wing.
81'Post update
Attempt blocked. Jack Cork (Burnley) right footed shot from the centre of the box is blocked. Assisted by Maxwel Cornet.
81'Post update
Foul by Callum Wilson (Newcastle United).
81'Post update
James Tarkowski (Burnley) wins a free kick in the defensive half.
79'Post update
Attempt missed. Wout Weghorst (Burnley) right footed shot from very close range misses to the left. Assisted by Ashley Barnes with a cross.
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Source: bbc.com