An early goal from Sone Aluko proved enough to earn City another three points in a drab Yorkshire derby which takes the Tigers to fifth in the Championship.
Aluko took a bad clearance from a corner on the byline, cut in and dispatched across keeper Luke Steele and into the far corner after 16 minutes.
City were wasteful for the rest of the game, with several chances going begging, allowing Barnsley to threaten in the second half, though ultimately their possession didn’t result in too many chances.
It was a sturdy if unexciting performance from the Tigers, who now face Wolves at the KC on Tuesday night. Match report later.