It was Grant Smith's second return to the County Ground since leaving last summer as he is now with Walsall, after joining Bristol City in the summer.
In the first half Swindon looked the better side and had a lot more of the chances with Cureton, Miglioranzi and Peacock all going close early on.
Ricky Shakes also came close for Swindon before Jamie Cureton scored his second goal for Swindon to 43 minutes with a volley from the edge of the area which beat the 'keeper and dipped just enough to creep below the bar and into the back of the net to give Swindon a deserved lead going into the half time break.
Walsall rarely looked like scoing, but did come close in the second half when they hit the bar from an angle, and the ball was cleared away. Rhys Evans had a quiet night as Walsall didn't look like scoring, and only had a few half chances all game.
Aaron Brown also went cose to scoing after beating a number of Walsall players he put in a cross which nearly went in anyway, but there was no one in the right place to score.
New loan signing Trevor Benjamin came on mid way through the second half to replace Lee Peacock. He had a good game, and won a few corners for Swindon.
The Walsall fans started to call for Paul Merson to be sacked as they are now starting to worry about relegation with Swindon looking to overtake them in the League One table.
Swindon had a number of late corners which they wasted, and one which they didn't even touch the ball before a Walsall player touched the ball first, so Swindon were given a free kick.
Swindon hang on to take all 3 points and move up at place to 22nd on 31 points only 2 points away from safety. Overall is was a good game with Swindon having most of the chances. On another day Swindon could have scored four or five goals from the number of chances they had. Swindon's next game is at home to Doncaster on Saturday.