The burly summer signing opened his account for Town in the 21st minute and added two more second-half goals as the Football League newcomers recorded a third successive league win, Barry Nicholson adding the fourth late on.
Parkin opened the scoring with a close-range finish after a mistake by Shrimps stopper Barry Roche.
The striker's second was a header from Andy Mangan's 50th-minute corner before he claimed his third - and the match ball - when again found by the excellent Mangan.
Barry Nicholson capped off a fine afternoon for the Cod Army with a fourth goal six minutes from time, Parkin turning provider with a far-post cross which was headed past Roche by the onrushing midfielder.
Morecambe struggled to create chances of their own, with their best effort coming in the 87th minute when substitute Jack Redshaw forced Scott Davies into an excellent save low to his left with a close-range flick.