Swindon still remain unbeaten in the league and cup since been beaten 3-2 by Sheffield Wednesday on the opening day of the season.
The game had been looking to be heading for a 0-0 draw before Andy Gurney scored a 40 yard shot with 12 minutes to go to beat the Wrexham keeper. Gurney had run with the ball from the half way line before striking to the ball to score what could be the goal of the season.
Earlier in the game Toomy Mooney had come close, but failed to get his shot on target, and on loan signing James Milner was also unlucky not to score his first goal for Swindon after going just wide.
Overall a good and vital win for Swindon after a run of 2-2 draws. The win now moves Swindon up to 6th in the second division before they play their next three away games which are at Grimsby on Tuesday evening, away at Barnsley next Saturday, and then another trip to Yorkshire when Swindon face Leeds in the second round of the Carling League Cup.