Port Vale scored first after only 14 minutes from a corner kick. This was the first goal Swindon had let in from a corner all season.
Port Vale then doubled their lead after 41 minutes when Steve McPhee shot beat Evans.
Swindon had few real chances to score in the first half, and at half time didn't look like they would get back into the game.
Swindon started the second half looking a lot better, with Rory Fallon joining Parkin and Mooney up front. After 50 minutes Fallon had Swindon best chance of the game so far when he hit the bar.
On 58 minutes against the run of play it looked to be all over for Swindon as Port Vale's McPhee scored from close range to make it 3-0 to the home side. The Swindon fans started to sing "we're going to win 4-3" and they were nearly correct.
On 63 minutes Sam Parkin pulled a goal back with a header making it his 20th goal of the season.
Matt Hewlett then gave Swindon a real chance when his 18 yard shot made it 3-2 after 68 minutes.
Port Vale hit the post, and Sam Parkin came close again for Swindon, before after 83 minutes super sub Rory Fallon scored from close range to complete Swindon's come back.
Fallon's goal now gives Andy King a selection problem ahead of this Saturday's trip to Peterborough as King now wants to play all three strikers, so will have to change the formation.
Overall this was a game of two halves with Port Vale being the better side in the first half, and Swindon looking a much better side in the second half. Although you wouldn't have thought it at half time Swindon were unlucky not to have scored a 4th or a 5th goal with a Parkin shot after just going wide after beating the Vale 'keeeper.