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:
9. Marcus Tavernier - 4
Struggled to create much playing just behind the strikers. Wayward free-kick summed up his first-half display. 4 Photo: Richard Heathcote
10. Marcus Browne - 4
Played alongside Fletcher but didn’t see much of the ball up top. 4 Photo: Jan Kruger
11. Ashley Fletcher - 5
Wasn't involved much and struggled to hold the ball up when it came his way. 5 Photo: Jan Kruger
12. Paddy McNair - 6
(for Dijksteel, 45) - Comfortable on the ball and created a few chances when stepping out from centre-back. 6 Photo: Alex Livesey