TWO second half thunderbolts ensured the Clarets parted the Riverside empty-handed.
An episode reminiscent of that two years ago when Tarmo Kink snatched the points for Boro with a couple of staggering strikes, Adam Reach and substitute Luke Williams obliged on this occasion with a stunning goal apiece.
The defeat will be hard to take for Eddie Howe's side who limited the hosts in the second 45-minute period, though Boro had the lion's share of possession.
Charlie Austin gave the Clarets the lead in the 41st minute when heading Kieran Trippier's deep cross beyond Jason Steele. But seconds later Boro were level when Nicky Bailey latched on to Curtis Main's cushioned header and rifled in to the corner from 25 yards.
It was a chess-like Championship encounter, with both Howe and Tony Mowbray adopting the same philosophy and matching each other tactically. The Clarets had the better of the opening exchanges, patiently working the ball from back to front, and they should have taken the lead when Sam Vokes found space beyond Justin Hoyte from Austin's neat pass and as the striker squared, Ross Wallace side-footed wide from the edge of the box with time on his hands.
The visitors continued to dictate the tempo, easing forward in to the final third, and Dean Marney's deflected effort looped wide following an intricate build up involving Junior Stanislas, Trippier and Wallace.
Vokes and Chris McCann both tested Steele with respective efforts that the keeper saved low to his right and left but then the home side grew in to the game.
Both sides were measured, methodical and patient in their approach, working the ball accurately and looking to force a way through with clever and calculated positional interchanges.
Loan man Josh McEachran almost found Adam Reach with a penetrative reverse pass that carved an entry through the Clarets rearguard, biut Lee Grant was on his toes to race out and claim possession.
Emmanuel Ledesma's floated free-kick had Grant scrambling to his near post moments later, but the set-piece dipped wide of the angle. Austin headed wide of the angle after leaping above Jonathan Woodgate and Rhys Williams from a Joseph Mills centre before Reach dragged wide from 12 yards after Ledesma's inswinging set-piece caused confusion among the Burnley defence.
As the half peetered out, looking goalless, the breakthrough arrived. Marney worked the ball out to Trippier and the full back's perfect cross was thumped home by Austin for his second goal of the campaign.
And the Clarets will be disappointed not to have clung on to that advantage at the interval when from the restart Bailey raced on to the loose ball and lashed in to the corner to make it 1-1.
After the break Boro were rampant while the Clarets proved ineffective. Mills fired wide of the near post from Trippier's centre after a pacey break from defence by McCann, but as the home side climbed in to control, Howe was forced to make a move, opting to pack the midfield with the addition of Marvin Bartley who replaced Vokes.
But the change had little impact on the flow of the fixture. Boro pressed and Grant was forced in to a superb save, turning Main's drive from distance around the post.
After Bartley was booked for an over-exuberant challenge in a bid to quell the pressure, Grant was called in to action again, this time tipping Woodgate's looping header over the bar from substitute Merouane Zemmama's free-kick.
Then, after Leadbitter pulled an effort wide of the post from 12 yards, Howe replaced Wallace with Ben Mee in search of a point. The move seemingly worked it's cause initially with the home side failing to force a route through.
But as the clock struck 80 minutes Reach responded with an impeccable effort that flashed past Grant and in to the far corner. However, Burnley forged a way back and levelled with three minutes of normal time remaining - Stanislas tapping home after McCann's header was cleared off the line from Trippier's inviting cross.
It looked like both sides would take a share of the spoils but in extraordinary fashion, Boro stole the points. Substitute Luke Williams shot a bullet beyond Grant from distance in to the roof of the net, the first of his career and a feat he is unlikely to reproduce again.