Martin Paterson's comeback gathered further momentum as his second goal in six days gave the Clarets a sixth win in seven games and a place just outside the play-off zone to end 2011 on a high.
Paterson's opportunist strike 11 minutes before half-time also gave Burnley a sixth successive win over a Hull side which must think they will never beat the Clarets again.
After letting a 2-0 lead slip against Eddie Howe's side back in November - a result which kick-started Burnley's remarkable run - the Tigers must have thought they had done enough in the return to gain some reward.
But while the fit-again Paterson took the plaudits, his defensive colleagues and revitalised midfielder Dean Marney, starring against his former club, produced the heroics to keep them out and secure a third successive clean sheet and a result which marks Burnley out as serious promotion contenders.
The Clarets did it despite an enforced defensive change as they sought to extend their winning run against the Tigers with Michael Duff's hamstring strain sustained in the Boxing Day win over Doncaster keeping him out.
Ben Mee moved inside with Brian Easton regaining a starting spot at left-back behind Keith Treacy, who also returned to starting duty for the first time in almost a month.
Pato fires home the winner and celebrates with Ross Wallace
And it was Burnley's back four which was the busier of the two, despite the Clarets' taking a half-time lead through Paterson.
A Matty Fryatt shot grabbed at the second attempt by Lee Grant inside the opening minutes hinted at Hull's attacking threat as Robert Koren and Aaron McLean provided dangerous support for City's top scorer.
But through a combination of gritty defending and a couple of slices of good fortune, the Clarets protected their goal with Jack Hobbs missing the visitors' best chance with just over half an hour gone as he side-footed wide.
And minutes later the Hull skipper must have been doubly rueing his miss as he gifted Burnley the lead.
Having survived another scare when McLean nodded wide, Grant powered his goal-kick up field where Hobbs was caught out by the bounce and made a mess of an attempted header back to goalkeeper Peter Gulacsi.
Jay Rodriguez has an effort is ruled out for off-side
Gulacsi could only parry the ball high above his head and Paterson needed no second invitation to pick up the loose ball and steer a shot into the unguided side of the net.
The on-loan Liverpool keeper played virtually no further part as he limped off to be replaced by Adrian Basso and the Clarets had a re-shuffle of their own at the break in terms of formation as Marney was deployed in a deeper role to keep tabs on Koren.
Jay Rodriguez moved wide in a midfield four but the move barely stemmed the flow and Koren should have levelled ten minutes into the second half.
Andy Dawson's low cross reached the Slovenian international just inside the penalty area but his deliberate finish sent the ball the wrong side of the post.
Koren was then off target again as he lifted a McLean cross over the top as the Clarets continued to live dangerously, despite the introduction of Marvin Bartley to further strengthen the midfield.
Ben Mee receives treatment as he keeps the Tigers at bay
But with the game becoming increasingly stretched Burnley could have snatched a second on the break to earn some welcome breathing space with 20 minutes to go.
Ross Wallace did everything right in cutting inside to deliver a perfect return pass to Paterson but this time the striker was unable to find the net as Basso dived to his right to block his effort.
Rodriguez then had another opportunity as he got in behind the Tigers' defence but the Clarets' top scorer was unable to pick out a team-mate with a low cross which fizzed in front of goal to make it a nervy finish.
It was backs-to-the-wall stuff at times combined with some desperate counter-attacks, Rodriguez slicing a volley wide after being superbly picked out by Wallace.
Three points and another clean sheet
But none of the misses proved costly as the Clarets' determination to keep their winning run going shone through again with another shut-out taking Howe's braves even nearer the top six.
Burnley: Grant, Trippier, Easton, Edgar, Mee, Marney, McCann, Wallace, Rodriguez, Paterson (Vokes 89), Treacy (Bartley 64). Subs: Amougou, Austin, Stewart.
Booked: Paterson 86
Hull: Gulacsi (Basso 42), Dawson, McKenna, Chester, Hobbs, Stewart (Brady 66), Evans, McLean (Garcia 83), Koren, Fryatt, McShane. Subs: Cairney, Dudgeon.
Booked: McShane 54
Referee: Chris Sarginson