The Tykes completely outclassed a limp Swindon outfit and could have scored more than the three goals which won them the game.
Andy Ritchie's side could hardly have wished for a better start after they took the lead after just eight minutes.
Paul Hayes broke free down the left and crossed for midfielder Martin Devaney to slip the ball past Tom Heaton in the Swindon goal for his third of the season.
Devaney could then have added a second just minutes later when he wriggled free inside the Swindon box only to blast high and wide with the goal at his mercy.
Swindon's only real response to Barnley's first-half dominance was when Hameur Bouazza failed to direct a header past Nick Colgan.
The away side grabbed their second on 51 minutes with a classic breakaway goal.
The impressive Stephen McPhail delivered an expertly weighted cross-field pass into the path of Chris Shuker.
Shuker continued unopposed towards the Swindon goal before firing low into Heaton's right-hand corner.
The midfielder then grabbed his second on 69 minutes, finishing off Marc Richards' knockdown.
Swindon failed to muster any real attacking threat until the last 10 minutes when Charlie Comyn-Platt fired a half-volley just wide of the post.
Top scorer Rory Fallon also went close with a free header from a corner but if either of these efforts had gone in it would have flattered the home team.
Fallon's afternoon got even worse when he was booked for gesturing to the Barnsley's fans after they taunted their former striker.