On 25 minutes Chris Llewellyn scored the first goal of the game beating Rhys Evans in the Swindon goal.
Swindon went into the half time break, having played against the strong winds in the first half still losing 1-0.
Sammy Igoe equalised on 49 minutes with a shot from outside the box beating the Wrexham 'keeper.
It wasn't long before Wrexham were back in the lead with a close range goal from Carlos Edwards, and on 68 minutes Wrexham had made it 3-1 when Steve Thomas beat the diving Evans with a 20 yard shot.
On 77 minutes Andy Gurney pulled a goal back for Swindon from close range, but the same as last week against Plymouth Swindon were unable to get a late equaliser despite so late pressure.
The defeat moves Swindon back a place in the table to 5th. Overall Swindon played fairly poorly, and Wrexham took their chances well to win the game, although Swindon did have chances to win the game.
Swindon's next game is at home to Barnsley next Saturday.