Lukas Magera and Mehdi Kerrouche scored in either half as Swindon moved up to sixth in League Two.
Spanish winger Lander Gabilondo created Swindon's opener as he cut in from the left and fed Magera, whose 20-yard shot flew inside the right-hand post.
The visitors added a second when Adam Yates fouled Magera in the box.
Kerrouche converted the resulting penalty two minutes after the break to condemn Micky Adams to defeat in his 100th game in charge of Vale.
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Port Vale manager Micky Adams told BBC Radio Stoke:
"It was another home disappointment. We're not finding the answers here for some reason and we've got to find the answers, because if we don't, it's going to be a long winter.
"Quite clearly there's a lack of confidence in certain individuals.
"It's about individual errors and at the moment individual errors are costing us."
Swindon manager Paolo di Canio told BBC Wiltshire:
"The discipline, the commitment and the encouragement they gave each other was absolutely amazing.
"We were always in control of the game, the opponents did not have one clear chance.
"Five clean sheets (in a row) is good but most important was three points."