Andraz Sporar opened the scoring for the Teessiders with a header in the first half, converting Paddy McNair’s inviting cross.
Neil Warnock’s side then had more opportunities to extend their lead before Matt Crooks made the game secure three minutes from time, heading home after Jonny Howson knocked the ball back across goal.
The result moves Boro up to 10th in the Championship table and just three points off a play-off position.
Barnsley, meanwhile, have dropped to 23rd in the Championship after a disappointing start to the season for their new boss Markus Schopp.
Warnock will now prepare for a meeting with his former club Cardiff this weekend.
Our reporter Joe Nicholson has delivered his verdict on how each player fared against Barnelsy at the Riverside.
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5. Jonny Howson - 7
Often drifted out to the right as Boro’s system altered in and out of possession. Plugged gaps defensively and made a few forays forward. 7
Photo: George Wood
6. Matt Crooks - 8
A few loose passes but played a key role winning the ball back and was tenacious in the heart of midfield. Made the game safe with a late goal. 8
Photo: Stu Forster
7. Marcus Tavernier - 6
Full of energy on the right but was often wasteful when he reached the final third of the pitch. 6
Photo: Stu Forster
8. Isaiah Jones - 6
Helped his side press higher up the pitch and attempted to take his opposite number on when he had the chance. Drifted in and out of the game. 6
Photo: Steve Bardens