Danny Ings' second-half winner was not enough to save Burnley from relegation out of the Premier League - and opponents Hull are now favourites to follow after this perilous defeat.
Results elsewhere conspired to doom the Clarets, who had gone into the KC Stadium clash knowing they needed a win to stand any chance of staying up, and that even that might not be enough.
Sean Dyche's men kept their side of the bargain with a gutsy display capped by Ings' 62nd-minute strike which ended a run of more than 10 hours without a goal.
But it proved a dismal afternoon for the Tigers, who now look in serious danger of joining Burnley in the Championship as they languish in the drop zone with games against Tottenham and Manchester United to come.
Robbie Brady twice slammed the woodwork from long-range free-kicks and substitute Abel Hernandez came close with a back-heel but the Tigers' performance lacked the buzz with which they had set about beating Liverpool less than two weeks ago.
Dyche paid tribute to his men after the match, despite seeing them sent back to the Championship.
"We knew statistically it was going to be tough and to stay alive so long has been terrific, but in the end we've just come up short," he said.
"I've been very proud of the players & a lot of things have moved forward at this club, but that doesn't take away the disappointment.
"I must mention our fans because they have been right with us every step of the way. That's how fans everywhere should be.
"We have been competitive in nearly every game and there is real resilience & growth in this squad and that bodes well for the future."
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