Parkin kept up his remarkable scoring rate for the Robins with goals in the 38th and 58th minutes, taking his tally for the season to 19.
He's now hit 68 goals in less than three seasons at the County Ground.
Right-winger Sammy Igoe supplied Parkin's ammunition on both occasions.
Parkin bundled in his diagonal cross for the first and Igoe pulled back an inviting low pass for the striker to sweep home a sweet right-foot shot for the second.
Leon Constantine stabbed in an opportunist opener for Torquay in the 25th minute after Paul Robinson nodded down Alex Russell's corner, but they were outgunned for most of the first half.
The Gulls, who lost skipper and centre-half Craig Taylor with a groin injury midway through the first half, might have crumbled after Parkin fired Swindon in front.
Instead they roared back, hit the bar twice through Russell free-kicks and scored a brilliant equaliser.
In the 63rd minute, Jo Kuffour dashed through from midfield and unleashed a 25-yard shot which screamed into the bottom left-hand corner.
It was Torquay, now unbeaten in five games, who did all the forcing in the last half-hour, Robinson sending a diving header over from Russell's corner.