Parkin had a loan spell with Oldhan during his early days at Chealsea and he inspired Swindon to score two goals in the last half hour of the game after Oldham had dominated.
The Latics fielded their youngest ever team with two teenagers in midfield. A striker making his debut and four more inexperienced players at the back. They were bright and lively in the first half but could not turn possession into more than one goal.
The new man up front was Manchester United striker Kenny Cooper who signed last week on a month's loan and the American marked his first start with a calmly taken goal after 14 minutes.
He swapped passes with Kevin Betsy and sent a sweetly hit shot inside the far post from 12 yards.
Oldham were firmly on top and Cooper forced a save from Rhys Evans before Lee Croft also brought the best out of Swindon's keeper.
At the other end Leslie Pogliacomi had to charge of his line to smother and effort from Jamie Slabber but it was his home team to threaten again when veteron David Eyres saw evans parry his free kick from right on the edge of the 18 yard box.
Swindon had kept themselves in the game and they capitalise on the hour through leading scorer Parkin.
His first shot was cleared off the line by 18-year-old Kelvin Lomax but Parkin got to the loose ball to head home from close range. He then had a hand in Swindon's winner by peeling off to the far post and heading back across to midfielder Grant Smith
Smith scored at the second attempt and his twelve yard shot bounced of the turf and over the helpless Pogliacomi.
Swindon nearly added a third when substitute Sam Igoe let fly from distance and they were able to hang on to three points without problems.