The first goal came after just four minutes when Callum McCormack scored from a well-drilled training ground corner routine. The second of the evening also came from a corner with Luke Mathews heading home from close range. Town's youngsters looked more than comfortable in possession and dominated throughout the first half and went into the break 2-0 up.
The second half saw Tom Smith miss a penalty. Two goals from Amir Gied along with a brilliant effort from Lee Marshall, who scored directly from a corner, wrapped up the win.
Manager Scott Lindsey called it "a disciplined and professional performance" that saw Swindon through to the next round.