Hull manager Peter Taylor failed with a £250,000 bid for Parkin during the close season and the former Chelsea striker showed what he had missed out on as he helped inflict a fifth away defeat on the visitors.
Parkin opened the scoring before netting his second and Swindon's third goal in the second half as they tore Hull apart by finding the back of the net three times in 16 minutes.
But it was Parkin's strike partner Christian Roberts who claimed the man of the match award as he set up two goals and scored another as Hull lost ground on leaders Luton.
Roberts was responsible for creating Swindon's first goal in the 21st minute as he crossed invitingly from the left for Parkin to head home unchallenged from six yards out.
Parkin could have scored two more soon after but wasted his opportunities and Hull substitute Jon Walters made him pay by equalising ten minutes before half-time with a deflected shot.
Tigers defender Marc Joseph was inches away from giving Taylor's side the lead in the 50th minute as he surged forward from right-back to force goalkeeper Rhys Evans to save his 25-yard effort.
But Hull had no answer to Swindon's surge after they had regained their lead with 17 minutes remaining.
Sammy Igoe had delivered a corner from the left which Hull failed to clear and captain Sean O'Hanlon was left with the simple task of side-footing home from two yards out for his first goal of the season.
Parkin extended the lead with two minutes left after once again being set up by the impressive Roberts before the latter deservedly got his name on the score-sheet a minute later.
Hull's leading scorer Stuart Elliott pulled a goal back in stoppage time but it was little more than a consolation as the visitors slumped to another defeat away from home.