Swindon had won only once in 14 previous outings in all competitions and when they swept into a 3-0 lead early in the second half, it looked plain sailing.
But Walsall, amid a lean run of their own, lit the fuse with two goals in quick succession and had Swindon hanging on by their fingernails in a thrilling finale.
Swindon's record of just one win since late October got a significant boost when they scored twice in the opening half hour.
Kevin Amankwaah opened Swindon's account after just eight minutes - loan debutant Gordon Greer, from Doncaster Rovers, laid back a left-wing cross from Jon-Paul McGovern.
It was Amankwaah's first goal for three-and-a-half years since 2005, when he was with Swansea City.
Swindon created several chances before Simon Cox doubled their lead with a 25-yard gem on the half-hour, volleying his 18th goal of the season into the top right-hand corner.
Shortly after half time Billy Paynter put Swindon 3-0 up, latching on to a pass by Lilian Nalis and driving a shot under the diving body of Clayton Ince who should have saved it.
Swindon looked to be coasting to victory, but the match turned dramatically on its head in the last quarter of an hour.
Walsall, one win in seven, suddenly sprung into life with Jabo Ibehre reducing the arrears 15 minutes from the end.
Richard Taundry set it up after a slip by Jerel Ifil and drilled his shot past Petr Brezovan.
Swindon suddenly lost their composure and were right on the back-foot when Troy Deeney cut the deficit further two minutes later.
With almost the last kick of the match, Alex Nicholls sent a rasping 20-yarder towards goal, only to see his shot taking an agonising deflection and flashed just wide of the target.