Swindon Manager Andy King saluted captain Andy Gurney after his brilliant solo effort had earned victory for the home side and handed Wrexham their first away defeat of the season.
There appeared little threat when Gurney collected possession from team-mate Tommy Mooney on the halfway line in the 78th minute.
But the combative midfielder raced 40 yards before cutting in from the left and curling a right-foot shot beyond goalkeeper Andy Dibble's reach and into the bottom right hand corner.
King said: "It was a wonder goal and that's exactly what Andy is capable of.
"He's a vital part of the team and I don't think he gets the credit he deserves some times.
"It was a very close game and I got the feeling the only way somebody would score is with a mistake or with a piece of magic.
"That's exactly what happened." Gurney almost added a second in the closing stages when his left-footed drive from the edge of the area flew narrowly wide of the post, while on loan Leeds midfielder James Milner was unlucky not to mark an impressive home debut with a goal.
Milner headed just wide from eight yards out in the 39th minute, while he looked to have opened the scoring ten minutes after the restart only for Dibble to somehow claw the ball away from his goal line.
But Wrexham enjoyed plenty of possession and had two great chances to earn at least a draw in the final four minutes.
Substitute Almond One, making his debut after joining the Welsh side at the start of the week on a short term deal, found himself unmarked just ten yards out only for his effort to be blocked by goalkeeper Rhys Evans.
One then set up fellow substitute Hector Sam two minutes from the final whistle, but England Under 21 international Evans again showed quick reflexes to save his low shot.