City were under the cosh for the opening ten minutes but a goal from Freddie Eastwood put City ahead. Barnsley did pull level but City were the better side in the second half and a goal from Julian Gray in the 67th minute was enough for victory.
"We got stronger and stronger as the game went on," said Chris Coleman to the media after the game.
"I think Barnsley are a good team, I watched them against QPR and Crewe they lost but they played good football. "Manager Simon Davey has brought some good players to this club. Coming into this game we knew it was going to be hard.
"In the second half we started better. We stopped making individual errors, our passing was better and we are delighted to come here and get three points. Teams will come here and lose points.
"It's always been a difficult place to come. They've got a good record here. Once they've settled they'll be a decent team."