Middlesbrough 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 before Boro produced a late rally with substitutes Mustapha Carayol and Curtis Main to the fore.
Steele was at full-stretch to turn Austin's first-time effort from the edge of the box behind after Brian Stock's shot from a Junior Stanislas corner was blocked by McManus.
Burnley right-back Kieran Trippier exerted his influence throughout the opening stages, glancing the roof of the net with a free-kick before cleverly beating Middlesbrough defender George Friend to loft a ball just beyond his onrushing team-mates.
The insipid nature of Boro's first-half display was in keeping with a side on such a dismal run, but Burnley were unable to fashion a clear opportunity until Marney met Trippier's near-post cross with a fine header that Steele was equal to.
The game's outstanding performer began the second half with a skilful burst into the box that was robustly but fairly ended by Steele, resulting in a period of treatment.
A Middlesbrough attempt on goal finally materialised with an hour played. Carayol drew a foul and a yellow card from Kevin Long and Grant Leadbitter drove wide from the resulting free-kick.
Recalled Boro full-back Nicky Bailey hacked down Chris McCann in an even more inviting position, coming perilously close to conceding a penalty, but Trippier curled past the post.
Austin handed Boro a let-off in the 78th minute when he fired over on the angle from close range.
He might have paid for his profligacy as Main bundled 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.