Grimsby twice went close in the first half when Nicky Featherstone saw his left-footed shot held by Wayne Brown and then Michael Coulson shot into the side-netting after Peter Sweeney had touched a free-kick to him.
The best chance of the half fell to Lowe, who raced through and beat Nick Colgan with a right-footed shot but saw the ball rebound to the keeper off the far post.
Grimsby surged ahead when interplay between Adam Proudlock and Featherstone released Aka Akpro, who fired past Brown.
But there was drama in the 90th minute when Rob Atkinson challenged Lowe and referee Geoff Eltringham pointed to the spot. Colgan got a hand to Lowe's shot but could not keep the ball out.