Swindon's first proper chance came after 17 minutes when a 20 yard shot fro Brian Howard hit the bar.
But it was Wrexham who took the lead after 24 minutes when Swindon didn't clear the ball away allowing Dennis Lawrence to score from close range.
In the second half most of the Wrexham fans behind their goal started a protest to their chairman who wants to sell their Race course ground, for most of the second half a large banner was held behind their goal saying Save the Race course for Wrexham FC.
Wrexham made it 2-0 after 72 minutes after a penalty for an off the ball incident involving Grant Smith, and Wrexham's Chris Armstrong. Armstrong took the penalty and scored.
In the final ten minutes Andy King bought on 16 year old Andy Caton, who nearly scored with his first touch. Caton did get on the score sheet when in injury time he scored from close range to make the score 2-1 to Wrexham.
Overall a fairly poor game, with Swindon not having that many good chances to score. Swindon's next game is at home to Luton on Wednesday night at the County Ground.