The Hatters may still be on minus 23 points after being docked 30 after coming out of administration, but they showed enough skill and commitment to stage an unlikely escape from relegation to the Conference.
There was little meaningful football in a scrappy first half but the game opened up after the break and there were plenty of chances at either end.
Ryan Harley thumped the ball over the bar from 25 yards in the opening minutes as Exeter City started the brighter side.
Luton came closest to breaking the deadlock midway through the half. Keith Keane's throw in found Claude Gnakpa in the box and the Frenchman turned and struck the ball against the foot of the post from ten yards.
Gnakpa then fired wide from 20 yards and Kevin Nicholls struck the ball over the bar from the edge of the box as Luton began to look increasingly dangerous.
Exeter's best chance came when Adam Stansfield's low cross was struck just over the bar by the unmarked Harley.
Luton were ahead two minutes after the break. Harley wasa judged to have fouled Gnakpa just outside the box and when Nicholls floated the ball into the box, Parkin rose highest to nod the ball powerfully past Paul Jones.
The Hatters grew in confidence after the goal and Lewis Emanuel forced Jones to save well with a fine strike from 25 yards.
Exeter pushed forward in search of an equaliser and Richard Logan had a header cleared off the line by former Grecian George Pilkington after out jumping goalkeeper Dean Brill.
Matt Taylor, Craig McAllister and Harley all went close late on for the Grecians, but there was no way back.