In his first game as captain Dean Lewington brought down Craig Easton in the closing stages and the former Reading hit-man kept his cool to give the Robins all three points.
The visitors had taken the lead early in the second half after former Swindon captain Sean O'Hanlon made a calamitous error that allowed Billy Paynter to tuck home.
Jude Stirling equalised soon after as he converted Mark Wright's cross.
Both teams went in search of the winner but it was Swindon who took all three points as Cox sent Gueret the wrong way from 12 yards.
It will be a tough loss to take for the Dons, who had the better of the game and missed some decent chances. The Robins will be delighted to claim their first away win of the season though.
The first half was slow, as the heat seemed to sap energy out of both teams. Nonetheless it was the Dons who had most of the possession and looked more dangerous.
Early on Sam Baldock was played through on goal but his shot was deflected narrowly wide.
They continued to keep the ball and, just before the 20-minute mark could have taken the lead when Michael Timlin completely missed Wright's cross. The ball fell to Peter Leven but, as he waited for it to come down, he was put under pressure and could only scuff his shot at keeper Phil Smith.
The Dons continued to press and made a superb break when Wright was put through on goal by Baldock's fine deft touch but, with the goal gaping, he delayed his shot and was forced to cut back. Baldock then played the ball across goal to Cummings who hit a curling shot just over the bar.
The home side's best chance came on the stroke of half-time though as Aaron Wilbraham rose superbly to meet Carl Regan's cross but his looping header cannoned off the bar.
The Dons started the second half well and moments before O'Hanlon's error he could have give his side the lead as got on the end of Leven's superb whipped cross, but his header was tipped wide by Smith.
Minutes later though the Robins took the lead as crazy play from the Dons provided the visitors with a simple opportunity.
They kept playing the ball across the back four nonchalantly and O'Hanlon just took too much time on the ball. Cox robbed him and ran through on goal before squaring for Paynter who stroked home coolly from 12 yards.
But the lead didn't last too long. And if Swindon's goal was generous then the Dons' equaliser could only be described as a gift.
Wright swung in a corner and keeper Smith simply missed his punch with the ball hitting the surprised Stirling and trickling in.
The game was more open now as both teams pressed for the winner
Timlin played Cox through on goal but from a tight angle his weak shot failed to trouble Gueret. In return O'Hanlon had another header that sailed over.
The game looked destined for a draw but with two minutes to go Lewington brought down Craig Easton in the box after the Dons had failed to clear Mark Marshall's cross and he clumsily sent him to the floor.
Cox stepped up to take the kick and he easily sent Gueret the wrong way to ensure all three points.