The Robins' top scorer struck with a trademark header 18 minutes from time to cancel out Gregg Blundell's 39 minute opener and spare Swindon from a third league defeat in a row.
Doncaster without an away win since October dominated a dire first half and could have been ahead as early as the 12th minute with the impressive Ricky Ravenhill firing just over from 20 yards.
Only a last ditch tackle from Swindon defender Andy Nicholas denied on-loan Leeds midfielder Simon Johnson his first goal for his adopted club in the 23rd minute.
Doncaster would have taken the lead less than 60 seconds later but for a brilliant save from Swindon goalkeeper Rhys Evans.
Michael McIndoe picked out Doncaster captain Nick Fenton with a right-wing corner and the captain's header was turned away one handed by Evans.
Parkin came closest to breaking the deadlock for the home side in the 27th minute with a 15-yard curler just past the left-hand post.
But Rovers took a deserved lead through Blundell's seventh goal of the season six minutes before the interval. Right-back James Price put in a pin-point cross for Blundell to head past Evans at the back post and into the bottom left-hand corner of the net.
Fenton was denied again on the stroke of half-time when Swindon defender Luke Garrard cleared his header off the line after a corner from McIndoe had again caught the Swindon defence napping.
Swindon looked a much improved side in the second half, but Doncaster goalkeeper Andy Warrington seemed to have earned his side victory with a fine save to deny Christian Roberts from close range in the 54th minute.
But Parkin cut short the visitors' celebrations, heading home his fourth goal in six games after a cross from substitute David Duke.