Martin Paterson equalised in the first half for Burnley
Relegation-threatened Burnley boosted their chances of survival after Brian Laws's side came from behind to win.
Kevin Kilbane headed home from close range after just two minutes to put Hull ahead before Martin Paterson's neat finish pulled Burnley level.
Midway through the second half Michael Duff won a penalty that was converted by Graham Alexander, who six minutes later scored from another spot-kick.
Wade Elliott's superb free-kick late on rubbed further salt into Hull's wounds.
Victory saw Burnley - only the second time they had won under Laws - climb above Hull on goal difference, but West Ham's win prevented the Clarets from moving out of the Premier League relegation zone.
Hull and Burnley are now four points off safety with West Ham and Wigan above them on 31 points, although the Latics and the Tigers have played a game less.
Hull must bounce back quickly - Dowie
Considering the turbulent week Burnley have just experienced after the humiliating 6-1 defeat to Manchester City and rumours of dressing room unrest, Laws's side could not have picked a better time to pick up their first away win of the season.
Burnley went into a huddle before kick-off, though they showed little cohesiveness in going behind after just two minutes.
Craig Fagan found space on the right wing and released Jozy Altidore whose looping cross was headed home at the back post by an unmarked Kilbane for his first Hull goal.
Burnley looked shell-shocked and possession during the opening stages was dominated by Hull.
A clash of heads between Duff and Leon Cort saw the visitors temporarily reduced to 10-men while the Burnley defender was patched up.
Even so, for all Hull's possession, chances were few and far between and it took nearly half an hour before Burnley keeper Brian Jenson was seriously tested.
Having previously appeared nervous and indecisive, the Burnley keeper bravely saved Altidore's close-range strike with his face, with Jimmy Bullard firing the rebound over the crossbar.
Against the run of play, Paterson hauled Burnley back into the game.
Right-back Tyrone Mears created the goal, sending in a left-footed cross which Paterson neatly brought down before swivelling and firing past Boaz Myhill.
Play was halted for several minutes as Andy Dawson received treatment for a shin injury before he was stretchered off following a Mears tackle, with Nick Barmby brought on to replace him and Kilbane switching to the defence.
Soon after, Burnley had a golden opportunity to take the lead but an unmarked Duff side-footed over the bar from close range after Paterson's cross had evaded Hull's central defenders.
Laws credits 'huge' win to players
Burnley took the lead in controversial fashion with the visitors allowed to take a free-kick twice, after Fagan was penalised for not retreating 10 yards.
The second free-kick from Danny Fox was floated into the Hull box and nodded down to the feet of Duff, who fell under pressure from George Boateng and Ibrahima Sonko, with referee Martin Atkinson pointing to the penalty spot.
Burnley captain Alexander made no mistake from 12 yards, firing the penalty to Myhill's left as the Hull keeper went the other way.
David Nugent won Burnley's second penalty when he was felled by Steven Mouyokolo, with Alexander again sending Myhill the wrong way from the spot, finding the top corner of the net with the outside of his boot.
In injury-time Burnley sealed the rout, with Elliott celebrating making his 200th appearance for the club by finding the top corner of the net with an inswinging free-kick from wide on the left.
Hull temporary football management consultant Iain Dowie: "There is a fragility about the place. We've got five games left and I will demand a response.
"We deviated from the game plan. But it is my responsibility and you have to take the brickbats. We will put in a display with more desire next week.
"Clearly it's not a result we would like to be associated with."
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