Chris Iwelumo and Chris Eagles both scored twice as the Tigers, who had not conceded in 279 minutes of Championship football prior to tonight, fell apart.
Hull won away for the first time in 30 attempts on Saturday, beating Norwich 2-0 at Carrow Road, but were on the back foot from the off this time.
Clarke Carlisle did well to slide in and block Tom Cairney's strike after Andre Bikey afforded him the opportunity to test Burnley goalkeeper Brian Jensen early on.
Iwelumo's flick-on shortly after had just too much on it for the fast-moving Jay Rodriguez, while the Clarets youngster almost connected with an Eagles chip a minute later as the hosts began to assert themselves.
Jay Simpson, making his 100th career league appearance, could and should have done better when volleying over the crossbar in the ninth minute after Nick Barmby had wriggled past Danny Fox down the right.
But captain Carlisle got back and did just enough to put the former Arsenal academy product off as he looked to steer beyond Jensen.
The Clarets deservedly forged ahead in the 14th minute when Wade Elliott slid Tyrone Mears in behind Cairney.
Mears drove for the byline and stood up an inch-perfect ball for Iwelumo to power beyond Matt Duke with his head.
A great block from Mears then denied Simpson before the Clarets doubled their advantage with just 25 minutes gone.
Jack Cork gave the home side the initial momentum, turning away from two players before involving Fox and Rodriguez in a lovely passing move.
Rodriguez provided the telling ball - a clever reverse pass to free Eagles, who made no mistake in sliding across Duke and into the bottom corner with his left foot.
Jensen beat away a Simpson drive from a tight angle, while Dean Marney charged forward against his old club and unsuccessfully tried his luck from 20 yards just before the break.
Eagles made it 3-0 in the 50th minute after Daniel Ayala inexplicably handled in the box as an Elliott cross dropped out of the night sky.
Referee Anthony Bates immediately pointed to the spot and Eagles, who took on penalty duties in Graham Alexander's absence, thumped the ball down the middle with Duke going the wrong way.
The Hull stopper spilled a deflected Rodriguez shot right into Iwelumo's path just four minutes later and he needed no second invitation to lash home his second of the evening and his seventh goal in a Claret and Blue shirt - all seven coming at Turf Moor.
Eagles went close from 40 yards and saw a curling effort deflected agonisingly wide as he chased his hat-trick.
Ross Wallace, Martin Paterson and Steven Thompson were all thrown on as Burnley tried in vain to improve their tally, Paterson spurning the best of the remaining chances.