The humble Lancashire club needed to win their last three games to have any hope of avoiding the drop but there proved no escape after Sunderland, Leicester City and Aston Villa all won and Newcastle United drew.
Manchester United won 2-1 at Crystal Palace to consolidate fourth spot, a first win in four games for Louis van Gaal's side ensuring they need only one point from two games to get back into the Champions League frame.
Sunderland's win over Everton sealed Burnley's fate but six other sides are still in trouble, including Queens Park Rangers and Hull who occupy the other places in the relegation zone.
QPR will be doomed if they fail to win at second-placed Manchester City on Sunday.
At the other end of the standings, United will join City, Arsenal and Chelsea in the Champions League next season if champions Chelsea beat Liverpool on Sunday.
United ended a run of three consecutive defeats when they won 2-1 at Crystal Palace thanks to a 19th-minute Juan Mata penalty and a 78th-minute header from Marouane Fellaini either side of Jason Puncheon's 57th-minute deflected free kick.
United are seven points clear of Liverpool, who have three games remaining.
IN VAIN
Danny Ings capitalised on slack Hull defending to score Burnley's first goal in over 10 hours but it proved in vain.
Ings, whose displays this season have earned plenty of praise, spoke for his team when he told the BBC: "The lads showed unbelievable fight and spirit today.
"I thought we were phenomenal and were on top from start to finish -- but it has come a little too late.
"Now we are going to play the last two games with pride and hope to finish strongly."
With bottom-placed QPR almost certain to join Burnley in the Championship, the battle to avoid the third and final relegation place is still very much alive.
Hull, Newcastle, Sunderland, Leicester and Aston Villa are separated by only four points.
Steve Bruce's Hull are 18th following the defeat by Burnley and they are two points behind Newcastle after John Carver's side ended a run of eight successive defeats with a 1-1 draw against West Bromwich Albion at St James' Park.
Victor Anichebe headed West Brom ahead but Ayoze Perez struck the equaliser just before halftime.
Sunderland claimed a vital 2-0 win over Everton at Goodison Park to climb out of the bottom three and level on 36 points with arch-rivals Newcastle, but Dick Advocaat's side have a game in hand on the teams around them.
Danny Graham was in the right place to deflect Jordi Gomez's shot past Tim Howard and record his first goal for the club he joined over two years ago before Jermain Defoe made sure of the points five minutes from time.
FIRING FOXES
Leicester have now won six of their last seven league matches and remain on course to avoid the drop after a comfortable 2-0 victory over Southampton.
Riyad Mahrez's low drive fired Leicester in front on seven minutes before the Algerian added a second 12 minutes later to move the flying Foxes up to 15th with 37 points.
FA Cup finalists Aston Villa rose to 14th after Tom Cleverley tapped home Jack Grealish's cross to give Tim Sherwood's men a 1-0 win over West Ham United at Villa Park.
Sixth-placed Tottenham Hotspur hold a point advantage over Southampton in the battle for Europa League qualification despite a 3-0 defeat against Stoke City.
First-half goals from Charlie Adam and Steven Nzonzi set Stoke on their way before Spurs defender Vlad Chiriches was sent off after the break and Mame Diouf added a late third.
(Editing by Ed Osmond and Martyn Herman)
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