Despite it being 'Lancashire Day', Sean Dyche's men spent the evening in Yorkshire but were unable to add to their one triumph on the Tykes' patch in 80 years.
Leading scorer Charlie Austin got the visitors off to a great start, ending a run of three games without a goal when powering a header beyond Luke Steele from Ross Wallace's corner in the fifth minute.
But in a game lacking any real conviction or quality, opportunities proved few and far between. Keith Hill's side pressed but seemingly lacked the craft or invention to penetrate, despite the best efforts of Craig Davies and Marcus Tudgay.
The Clarets could have doubled their advantage when Austin cleverly turned former Burnley defender Stephen Foster down the left and centred for Chris McCann who lifted his header over the bar under pressure from Jimmy McNulty.
Both sides showed promise on the break but often faltered in the final third, with poor distribution from the flanks proving costly. Austin desperately threw himself at McCann's cross at the back post after the Dubliner had combined with Ben Mee before Wallace sliced harmlessly wide from distance.
The Clarets looked comfortable, rarely troubled by the home side, but out of nowhere the Tykes drew level. Full-back Scott Golbourne fired a deep cross in to the box and Tudgay rose above skipper Jason Shackell to glance the ball over Lee Grant and in to the back of the net - his first goal since January.
And in the closing stages Akos Buzsaky profited from a wayward clearance but rifled an angled drive past the far post before referee Kevin Wright ended the half with the two sides level at 1-1.
The second half display proved to be equally as ugly, with neither outfit able to forge a convincing passage of play or a clear opening. With both defences holding firm, absorbing attacks with ease, speculative attempts from distance became a familiar occurence.
The first effort of the second stanza arrived in the early stages as Martin Paterson, playing out another relatively anonymous performance, span McNulty on the edge of the box but his timid strike floated in to the arms of Steele.
The Clarets went close again when Danny Ings, who replaced Marvin Bartley after the break, collected the ball after McCann's cross was cleared before drilling a low attempt beyond Steele which cannoned back off the post. It was a break Ings so desperately needed as he searches for his first goal since returning from a knee injury.
Davies was the next player to try his luck when gifted too much space but his stinging right-footed drive flashed across Grant and whistled past the post. The Clarets struggled to make the ball stick, failing to find their characteristic rhythm and swagger and it was the home side that pushed.
Grant was equal to substitute Jim O'Brien's volley after Tudgay had provided a cushioned assist while either side of that attempt the Clarets keeper denied playmaker Buzasky, the second to deny a bending free-kick from 20 yards after Michael Duff had chopped down loanee Emile Sinclair who broke late on.
Rovers boss Henning Berg was in the stands taking notes ahead of the weekend's derby, and Dyches’ team will expectedly return the favour when Bolton are the visitors to Ewood Park tomorrow evening. But the Clarets will have to be better if they hope to beat Rovers for the first time since April, 1979.