Tony Thorpe came close for Swindon in the first few minutes, but Swindon's best chance came on 10 minutes with Swindon just going wide.
Barnsley then took the ball up the other end of the pitch ans opened the scoring for themselves after 11 minutes when Paul Hayes beat the offside trap after a mistake by Jerel Ifil for his shot to also beat Evans from the edge of the box to make it 1-0 to the Yorkshire side.
On 21 minutes Barnsley really should have made it 2-0 when Sean O'Hanlon bought down Paul Hayes in the box, and Barnley were awarded a penalty. Daniel Nardiello took the penalty for the home side, but Evans dived to his left, and saved the shot.
For the rest of the half there were few chances for either side with Swindon not even having a shot on target, and Barnssley never looking like the would get another goal.
However Barnsley doubled the lead on 47 minutes when Chris Shuker was able to score from a tight angle to make it 2-0.
Swindon came close to scoring on 55 minutes when their first shot of the game was handled on the line by Robbie Williams, who was sent off for hand ball, and Swindon were given a penalty, but for the second time in under an hour the penalty by new signing Jamie Cureton was saved.
Roberts came on for the final 25 minutes for Swindon replacing Michael Pook. Roberts should have scored for swindon late on, but his shot had far too much power so went wide.
Overall a fairly average game. Swindon seem to be missing Sam Parkin up front. Barnsley were not that good a side, but took their chances well. Swindon's first home game of the season is on Tuesday night against Oldham.