Aden Flint had already put the hosts ahead when Dani Lopez left referee Gary Sutton with little option but to send him off after the Stevenage striker petulantly raised his hands to Swindon skipper Alan McCormack five minutes before half-time.
Boro were already facing a tough task to haul themselves back into the game after Flint reacted sharply to fire the Robins in front. Stevenage failed to clear McCormack's sliced shot and the central defender stuck out a leg to force the loose ball home for his second goal of the season.
Although the visitors offered little threat going forward, Swindon were relieved at the breathing space Gary Roberts' goal gave them after 53 minutes.
The Robins worked the ball to Roberts who turned sharply to buy himself a yard of space to rasp in a shot which took a slight deflection to take the ball out of the reach of goalkeeper Chris Day.
Day then stuck out a leg to deny Roberts a second but it was only a reprieve as a rampant Swindon were rewarded for their pressure with a third goal.
Stevenage again failed to deal with a set-piece and when the ball fell to Flint he fired home from 12 yards out.
Swindon keeper Wes Foderingham was largely unemployed, with his only action in the first half as he tipped Mark Roberts' looping header on to the top of the crossbar.
In contrast, Day produced a great save from Swindon sub James Collins to deny the Robins a flattering fourth.