Goals by Swindon skipper Simon Ferry and Matt Ritchie in either half were enough to hand the Saddlers their second defeat in a five days at the Banks's Stadium.
Ferry struck in the first 57 seconds of the match, lashing home a cross from Gary Roberts to hand the visitors a dream start.
Richard Taundry's block prevented James Collins adding a second midway through the first half but Town made sure of the points in the 62nd minute, Walsall's debutant full-back Malvind Benning blocked a shot from Miles Storey and Ritchie was on hand to crack home the rebound.
The hosts never gave up but rarely looked like scoring, Adam Chambers sending one volley over the bar while their best effort came courtesy of Jamie Paterson's 61st-minute free-kick which was well saved by Wes Foderingham.
Swindon were always dangerous on the break and with 11 minutes remaining home 'keeper David Grof did well to deny Andy Williams when clean through.