Tony Mowbray's play-off occupants headed into the contest bearing a grim form sheet of six defeats in their last seven npower Championship matches.
They spent the vast majority of the 90 minutes at Turf Moor on the back foot, with goalkeeper Jason Steele saving well from Charlie Austin and Dean Marney in the first half.
But Burnley, 10th in the table and seven points behind their opponents with a game in hand, could not turn their dominance into the required amount of clear-cut chances.
Top scorer Austin spurned their best opening of the second period when he fired over on the angle from close range after 78 minutes.
He might have paid for his profligacy as Curtis Main bundled fellow substitute Mustapha Carayol's cross past the near post before volleying onto the roof of the net.
Carayol gave Burnley goalkeeper Lee Grant his first serious work of the evening in stoppage time with a swerving, dipping long-ranger that was tipped over.
Following four-goal defeats on the road to Ipswich and Crystal Palace, this clean sheet comes as a boost to Mowbray, although Boro now hold only a two-point advantage over seventh-placed Brighton having played a game more.