Burnley down and Hull set to follow
Danny Ings' second-half winner was not enough to save Burnley from relegation out of the Barclays 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.
Knowledge of Sunderland's lunchtime win at Everton - which ensured Hull would start the game in the drop zone - can hardly have helped the atmosphere of tension as Steve Bruce's side were largely frustrated during a tight first half.
The visitors, for whom the mathematics of survival meant a win was the very least they required, were roared on by a defiant contingent of travelling fans but they too appeared short on ideas.
Despite Stephen Quinn's third-minute cross narrowly evading Ahmed Elmohamady in front of goal, most of City's early play lacked the necessary sharpness.
James Chester had to be alert to deny Ings a shooting opportunity after a clever through-ball from Ashley Barnes, but the Clarets showed few signs of grabbing the goal they needed to prolong their survival fight.
Brady consistently posed problems down the left and in the 19th minute he got behind the Burnley defence and sent in a low cross which was cleared off the line by Jason Shackell.
As the half went on Hull gained the ascendency, with Elmohamady heading just over from a Brady cross and Paul McShane also inches away with a header from a Brady corner from the left.
Brady himself had his first chance to become Hull's hero in the 37th minute when he clattered the top of Tom Heaton's bar with the first of his free-kicks.
Burnley boss Sean Dyche clearly took the decision to start to stretch the game at the start of the second half - although the way other results stood at the interval, even a winner would not have been enough to save them.
Ashley Barnes sent an overhead free-kick crawling just wide of Steve Harper's right-hand post and Matt Taylor also came close before the visitors had a penalty appeal turned down when Ings tumbled under McShane's challenge in the box.
Hull boss Steve Bruce threw on Nikica Jelavic on the hour and played three up front but two minutes later Burnley snatched a shock opener when the home defence failed to deal with Ben Mee's ball into the box and Ings rifled home.
Hernandez, introduced moments earlier for the ineffective Sone Aluko, came close with a neat back-heel which was held well by Heaton then Brady rattled the bar for the second time from a long-range free-kick.
Bruce's side launched a series of increasingly desperate attacks as the minutes ticked by but the Tigers were frustrated and will now have everything to do in their last two games if they are to avoid joining their opponents in relegation to the Championship.