The game started slowly with neither side having any real shots on goal in the first half.
Swindon's only chances in the first half came from crosses, but although Smith, and Jamie Slabber starting his first game for Swindon came close Swindon never really looked like scoring.
Swindon 3 Stockport 0
Swindon's best chance in the first half was when Sam Parkin found the ball at his feet from 15 yards out, but he took to long over his shot, and the ball was cleared away.
On 60 minutes Grant Smith came close to scoring, but his shot was tipped over the bar by the 'keeper for a corner.
Swindon took the lead from the corner on 61 minutes when the ball fell to Matt Heywood was scored his first goal of the season to make it 1-0.
Then two minutes later Swindon had another corner which was taken by Grant Smith, and Sean O'Hanlon headed in the cross from 12 yards out to make it 2-0.
Then seconds after the re-start Grant Smith had a shot from 30 yards out, the ball went through all the Stockport defence, and beat the 'keeper to make it 3-0 to Swindon. These 3 goals were all scored in under 4 minutes which was much quicker than the 10 minutes it took the put 3 past Sheffield Wednesday, and even beats the 5 minutes it took in 1998 to go 3-0 up against Bristol City.
Sam Parkin came close to adding a 4th goal minutes later, but the final score finished 3-0, with Stockport who are bottom of the table not having their first shot on target until the final ten minutes of the game.
Rory Fallon on as a sub also came close late on to heading in another Smith corner, but the ball went just wide.
Overall most of the game was fairly average, and apart from the 4 minute spell neither side had many chances of scoring, but Swindon came away with an important 3-0 win which sees them just 5 points of the play off's.
Swindon's next game is away to Oldham next Saturday.