Both teams struggled to keep the ball on the ground, but Grimsby created the better chances.
The Mariners were denied two penalty appeals and had a stoppage-time goal disallowed.
In contrast, Lincoln, without a win since boss Keith Alexander took the November manager of the month award, rarely looked like scoring.
The Red Imps' best chance came in the first ten minutes, when striker Francis Green hit a dipping 20-yard half-volley which flew inches over the bar.
But Grimsby were quickly in control again with Andy Parkinson and Terry Fleming both having shots charged down. Then Ronnie Bull hammered a 25-yard free-kick over the bar.
Lincoln hit back early in the second half, but when Ciaran Toner slipped a low cross into the heart of the Town defence, Simon Yeo was just unable to make contact.
Toner smashed a long-range effort into the side-netting but as the game opened up, Grimsby looked likelier to score.
New signing Martin Gritton broke away in the 62nd minute, but Lincoln keeper Alan Marriott held his low shot.
With 16 minutes left, Fleming hit a tremendous shot from inside the box which looked to be heading for the net until Marriott pulled off a superb save.
Ashley Sestanovich then floated the ball into the Lincoln box and Fleming, who was playing against one of his old clubs, was inches away from making contact.
Grimsby midfielder Jason Crowe had an excellent chance to settle the game in the 82nd minute. He broke through two tackles and burst into the box, but Marriott somehow kept his shot out.
Lincoln became increasingly desperate with skipper Paul Morgan and midfielder Richard Butcher both shown the yellow card for late fouls.
Town, already frustrated by the referee for turning down a first-half penalty shout, had another appeal rejected with three minutes left when Gritton went down in the box.
There was more disappointment for the Mariners in the third minute of stoppage time when Lincoln only half-cleared a corner, and Town substitute Michael Reddy blasted a low shot home.
But as the visitors celebrated, the referee awarded Lincoln a free-kick for an earlier infringement.