Sam Mantom was also on target as the Saddlers comfortably swept aside their play-off rivals.
Swindon started brightly and Nile Ranger had an acrobatic overhead kick cleared off the line by Craig Westcarr early on.
But it was Walsall who took the lead after 17 minutes when Hemmings took advantage of some sloppy Swindon defending to rifle in from the edge of the box.
The visitors doubled their lead two minutes into the second half thanks to Mantom's second goal of the season.
Westcarr's initial shot was beaten away by Swindon goalkeeper Wes Foderingham and Mantom was on hand to slot home the rebound.
Hemmings added his second and Walsall's third 11 minutes from time when he skipped through the Swindon defence and slotted past Foderingham.
Ranger did pull one back with an 83rd-minute header but it was too little too late for Mark Cooper's side.