Goals from Patrick Schmidt and Jordan Williams saw the Tykes progress on Teesside, setting up a third-round meeting with Chelsea.
Our Boro writer Joe Nicholson has dished out his marks following the match – scroll down and flick through the pages of our our picture gallery to see if you agree with the ratings:
1. Marcus Bettinelli - 4
Was beaten at his near post twice in the first half when he was left exposed by his defenders. 4 Photo: George Wood
2. Hayden Coulson - 4
Allowed Williams to run in behind him for Barnsley’s second goal. Didn’t look comfortable in a right wing-back role. 4 Photo: George Wood
3. Anfernee Dijksteel - 6
Looked composed on the ball once again and calmly averted a couple of Barnsley attacks. Was subbed at half-time. 6 Photo: Richard Heathcote
4. Dael Fry - 5
Captained the side but wasn’t overly convincing as Boro were picked apart in the first half. 5 Photo: Alex Davidson