Goals from Rouwen Hennings and Stephen Ward saw the Clarets fight back from a goal down to beat Boro at the Riverside in the third round of the FA Cup.
The Clarets, who had won just once in 14 outings on the road in the competition prior to the tie, hadn't reached the fourth round since 2011 where they were beaten 5-1 against West Ham United at the Boleyn Ground.
Defeats against Norwich City, Barnsley, Southampton and Spurs followed in respective seasons.
Burnley boss Sean Dyche rang the changes for the tie in Teeside with Hennings, Frederik Ulvestad, George Boyd and Tendayi Darikwa stepping in for Andre Gray, Joey Barton, Scott Arfield and Matt Lowton.
And Boro boss Aitor Karanka also transformed his XI, making seven changes from the side that beat Derby County 2-0 in the first game of 2016.
But the switch in personnel didn't seem to have any bearing on the hosts, who are cruising at the top of the Championship.
Last season's beaten play-off finalists were dominant throughout, creating incisive passages of play that often had the Clarets defence troubled.
Carlos De Pena struck wide from the edge of the box early on and the Uruguayan failed to beat Tom Heaton at his near post after taking down Diego Fabbrini's cross.
Adam Forshaw tried his luck with a right-footed strike from 25 yards out but the ball climbed over the bar as Heaton sprawled towards his upright.
Boro weren't short of options on either flank and skipper George Friend was proving particularly menacing for Darikwa.
The full back moved goal side at will, but his pull back wasn't quite accurate enough for Fabbrini who had pulled free on the penalty spot.
With the Clarets on the back foot, generally camped in their own half, Boro continued to apply the pressure.
Heaton was wrong-footed from Albert Adomah's deflected drive that crept wide after the Ghanaian winger manufactured space inside the box by dropping a shoulder and shifting the ball on to his left boot.
The Clarets skipper then foiled Fabbrini who had penetrated through the heart of the away side's rearguard.
The home side should've edged ahead in the 27th minute and, with nine goals already scored against the Clarets, you'd have backed David Nugent to find the net.
The striker, who made 20 starts for Burnley in a loan spell during the 2009/10 term, raced clear after Fernando Amorebieta's header had caught the visiting backline static but Heaton spread himself well to save.
There was little Heaton could do to prevent Boro from opening the scoring with 10 minutes of the half remaining, though.
The England international did make a stunning point blank save to deny Nugent from Friend's assist but Fabbrini was on hand to poke the rebound over the line.
With chances at a premium after the breakthrough it seemed as though the hosts were heading towards the interval with the advantage. However, it didn't work out that way.
Posing their first genuine threat of the half, an unmarked Hennings diverted Sam Vokes's cross beyond Tomas Mejias in the first minute of stoppage time to level proceedings. It was the first time that Boro had conceded in over 10 hours of football.
Burnley were much brighter in the second half. The visitors were more organised, kept their shape well, proved more economical in possession and gave the hosts something to think about.
Mejias did, however, remain relatively unexposed, though Vokes smashed wide of the near post from the angle of the penalty area early on.
Heaton remained the busier of the two goalkeepers, saving Fabbrini's angled drive and beating Adomah's stinging strike to safety.
Forshaw had a golden opportunity to restore Boro's lead but somehow guided his header well wide when unmarked from Adomah's delivery.
And they paid the price for that glaring miss in the 72nd minute as the Clarets took the lead. David Jones's corner was put back in to the mix by Boyd and Ward seized on the opportunity instinctively to steer his volley in to the roof of the net to make it 2-1 and provide the passage to the next round.