Lee Clark's side, a division above their hosts, had looked comfortable after Lee Novak fired home in the 22nd minute only for two first half defensive errors to gift Swindon an undeserved half-time lead.
With nine minutes to go before the break, Aden Flint swooped at the back post to nod in Simon Ferry's flick-on from Matt Ritchie's free kick.
Things got even better for the Robins three minutes later as Raffaele De Vita was on hand to sweep home from six yards after midfielder Ferry pulled the ball across the box.
After the break the visitor continually struggled to breakdown a stout Swindon defence, with Wes Foderingham rarely being called into action.
Substitute Mehdi Kerrouche finished a wonderful flowing counter attack in the 76th minute to put Paolo Di Canio's side in control before Ferry completed the rout from close range.