Parkin stooped to nod Arron Davies’ low cross into the net from 12 yards with 11 minutes remaining at St James’ Park and claim a deserved win for the hosts.
The Grecians had been the better of the teams in the first half, but without testing Rovers goalkeeper Steve Mildenhall.
Parkin and strike partner John O’Flynn were both off target with City’s best efforts, while Oliver Norburn fired a free-kick over the bar with Rovers’ only effort of the first half.
The opening goal came just before the hour mark when former Rovers defender Danny Coles powered a header into the roof of the net from Craig Woodman’s corner, but the lead lasted less than 10 minutes with Eliot Richards converting from close range after good work by Ellis Harrison.
The game seemed destined for a draw as Exeter lost their way, but the introduction of Alan Gow and Parkin’s header was ultimately the difference.