Goals from Jonny Howson and Chuba Akpom either side of half-time gave the Teessiders all three points before cauley woodrow scored a late consolation goal from the penalty spot.
Our Boro writer Joe Nicholson has dished out his marks following the match – scroll down and flick through the pages of our picture gallery to see them:
5. Marc Bola - 6
A few erratic crosses early on but improved going forward. His delivery led to Boro’s second goal. 6 Photo: Alex Davidson
6. Marcus Tavernier - 7
Adapted well after he was moved to right wing-back. Did well to wriggle into a shooting position before his shot was saved and Akpom converted. 7 Photo: Getty Images
7. Jonny Howson - 7
Scored his first goal of the season after finding space in the area. A disciplined display in midfield until he gave away a late penalty. 7 Photo: Getty Images
8. Sam Morsy - 7
Battled well in midfield and played a few forward passes which nearly opened Barnsley up. Still feels like there is more to come. 7 Photo: Owen Humphreys