The first half saw Huddersfield have more of the play with Brezovan having to make a number of good saves to keep the score level at 0-0 going into half time.
On 51 minutes Michael Collins opened the scoring for Huddersfield after hitting the left hand post the ball when it to make it 1-0.
Andy Butler made it 2-0 on the hour mark.
Then on 65 minutes Partick Kanyuka was shown a red card for holding back a Huddersfield player just outside the box.
Deep into injury time Simon Cox pulled a goal back for Swindon with a goal from the edge of the area, but it was too little too late for Swindon.
Swindon now have another 10 day break from the league before Walsall visit the County Ground in the next game.