Peterborough's lead didn't last long as a minute later Mayy Heywood found the ball at his feet from 15 yards out and he was able to fire the ball into the back of the net.
After 20 minutes David Farrell put Peterborough back in front.
For the rest of the first half Swindon were restricted to a few long distance half chances, but they never really looked like scoring.
At the start of the second half Rory Fallon came on, which was the third game in a row where he's come on at half time. This time he replaced Sean O'Hanlon.
Fallon had a few chances to score, the best coming on 51 minutes with a shot that went just wide.
Sam Parkin equalised on 64 minutes with a header which lobbed the advancing Peterborough 'keeper. This was Parkin's 21 goal of the season.
Posh sub Richard Logan put Peterborough back into the lead on 74 minutes with a close range shot from a corner.
Peterbough also had a goal disallowed and hit the post, but it was Swindon who pushed forard for the final 10 minutes to try and get an equaliser, but Peterborough scored a 4th on 89 minutes with a long distance lob over the op of Bart Griemink from 40 yards by Steve Thomson.
Overall Peterborough deserved their win as Swindon failed to control the game, and didn't create anything like the usual number of goal scoring chances.
Swindon's next game is the local derby against Bristol City at the County Ground this Saturday.