Prior to this the Saddlers had won nine and drawn one of their ten matches at Bescot Stadium, but they never looked like taking anything from this top of the table clash after going behind in the 23rd minute.
Swindon, who are third in the table, registered their fifth win in the six games that Paul Sturrock has been in charge and thoroughly deserved to do so.
Yet is was Walsall who were the first to go close to scoring in the 15th minute. Mark Kinsella, playing his last match before joining the coaching staff at Charlton Athletic, sent over a superb in swinging corner which was hooked goalwards by Chris Westwood, but the visitors' midfielder Sofiane Zaaboub cleared off the line.
Swindon always looked the more positive however, with Curtis Weston sending a header over from a cross by Zaaboub seconds later.
Swindon went in front with Lucas Jutkiewicz's first senior goal. The 17-year-old ran on to a throughball by Weston, easily beat defender Ian Roper for pace and slid a low shot past the helpless Clayton Ince.
Walsall showed little creativity in midfield and were too narrow as they endeavoured to get into the game.
On 34 minutes Daniel Fox forced keeper Phil Smith into a save with a 25-yard shot, but Swindon remained in charge.
Four minutes after the interval Walsall had a good opportunity when the hard working Kinsella crossed from the left, but Michael Dobson's shot from 20 yards went much too high.
Walsall lacked ideas, with front runners Martin Butler and Tommy Wright scarcely getting into the game and it was no surprise when the visitors increased the lead in the 68th minute,
A slip by Roper on the halfway line enabled the outstanding Jutkiewicz to run clear and the teenager was brought down in the box by Scott Dann. Roberts stepped up to score from the penalty spot.
In the 73rd minute Roberts produced a save from Ince and with the game heading into added time, there was a rare threat from Walsall when a shot by substitute Craig Pead hit the crossbar.