Unlikely hero David Edgar set up a thrilling fightback as three goals in the last 15 minutes, including an injury-time winner from Jay Rodriguez, gave the Clarets a dramatic and potentially season-changing win.
Trailing to two goals from Hull City top scorer Matty Fryatt, Burnley were sliding into the relegation zone on the back of what looked like being a fifth successive defeat.
But Edgar chose the perfect moment to score his first goals for the Clarets with two in the space of four minutes to completely re-write the script.
The Canadian international lit the touch paper for an explosive finale with two top-class finishes, one with his head and one with his right foot which would have made any striker proud.
And Eddie Howe's men - stung by last-gasp goals in their last two games - made it three straight wins at one of their happiest of hunting grounds with a late one of their own as Rodriguez showed nerves of steel to ram home the winner with his tenth goal of the season.
Howe had recalled Ben Mee and Junior Stanislas and employed Marvin Bartley in a deep lying midfield role in a bid to stop the rot with two changes from the side sunk by Birmingham in mid-week.
And birthday boy Stanislas could have celebrated with an early goal in a decent start from the Clarets.
Two-goal hero David Edgar
But the former West Ham man, 22 today, failed to make the most of the first chance when he slipped in the box and then blazed over from 16 yards with just goalkeeper Peter Gulacsi to beat.
Burnley looked comfortable enough but with virtually their first attack of the game, the Tigers pounced to go in front after 11 minutes.
Former Manchester United youngster Cameron Stewart created the chance as he sprinted past Kieran Trippier and when his low cross was delivered on a plate for Fryatt, City's leading marksman couldn't miss from inside the six-yard box.
With a miserly defensive record on their own patch, Hull were never going to make it easy for the Clarets to get back into the game as they looked comfortable in possession and happy to play on the break.
But Burnley, swapping and changing across their midfield to try and find a way through, did have a chance to level before half time when Stanislas was again given a sight of goal.
Matty Fryatt puts Hull 1-0 up
But rather than test Gulacsi on the volley, he opted to try and find lone striker Rodriguez and the opportunity went to waste.
And with the last kick of the first half Hull almost doubled their lead as Robbie Brady jinked his way into the box and forced Lee Grant to make a smart save low down to his right.
Howe reacted at half time by swapping Sam Vokes for Stanislas and going back to a 4-4-2 formation to try and give the Tigers something to think about.
Within five minutes Burnley were inches away from being level as Rodriguez struck a superb volley on the turn following Mee's long throw which smacked against the bar via the slightest of touches from the impressive Gulacsi.
But with Hull happy to soak up any pressure and then try and score on the break they did just that to go 2-0 up and seemingly put the game beyond Burnley's reach.
Edgar launches the fightback
Robert Koren was the architect after the Clarets had surrendered possession but Fryatt's angled shot should never have beaten Grant, whose attempted one-handed parry merely helped the ball into the net.
Suddenly Hull released the handbrake and Fryatt had a chance to complete his hat-trick from another Koren pass but this time his weak finish didn't trouble Grant as the Clarets found themselves badly stretched as the Tigers went for the kill.
Burnley were staring down the barrel at that point and Wallace's fifth booking of the season for a foul on Stewart means the winger must serve a one-match ban.
But Wallace almost gave the Clarets a glimmer of hope with 25 minutes to go when he curled a shot only inches wide after Vokes and Rodriguez had combined well to set up the chance.
Grant's save from the lively Koren at the other end then kept Burnley interested and with 12 minutes to go the possibility of a comeback was on when Edgar scored only the eighth opposition goal on Hull territory this season.
Well done mate
The previously watertight City defence failed to deal with a free-kick and when Wallace helped the ball across goal, Edgar reacted quickest to head beyond Gulacsi and into the far corner.
With roles reversed it was Hull taking on water and the Clarets capitalised in dramatic fashion as Edgar remarkably made it two goals in quick succession with a predatory finish as the defender spun onto a flick-on from Vokes, followingTrippier's long throw, and rifled a shot into the roof of the net.
The Clarets looked like a new team and rather than just settle for a point they pressed on for the winner which Keith Treacy thought he had scored in the 89th-minute with a stinging drive which Gulacsoi somehow finger-tipped around the post.
Thanks for coming
But with three minutes of added time to go, there was still an opportunity to nick a fourth away success of the campaign and incredibly the Clarets took it as Rodriguez raced onto a Chris McCann ball over the top to superbly steer a low shot into the bottom corner and breathe new life into Burnley's crazily unpredictable season.
Burnley: Grant, Trippier, Mee, Duff, Edgar, Bartley, McCann, Wallace (Amougou 90), Treacy, Rodriguez, Stanislas (Vokes ht). Subs: Hines, Easton, Stewart.
Booked: Wallace 51
Hull: Gulacsi, Rosenior, McKenna, Chester, Hobbs, Stewart (Dawson 77), Evans, Koren, Fryatt, Brady (Adebola 87), Dudgeon. Subs: Cairney, McShane, Basso.
Booked: Evans 77
Referee: Anthony Taylor