Wrexham six games without defeat are making a valiant effort to escape the drop and could have done the cause a great service in the last minute when substitute Michael Proctor hit inches over the bar when it looked as though the Dragons were going to get all three points.
The Dragons had an escape however minutes earlier when two substitutes combined to almost clinch it for the visitors. Gary Jones could not get a proper shot following a Paul Bolland header and the chance went begging.
Both sides found it difficult in the swirling wind and on a bumpy sandy pitch but Wrexham's Stuart Nicholson saw an effort cleared off the line in the opening minutes by Ciaran Toner.
Just before the break Wrexham's keeper Gavin Ward stopped Toner from breaking the deadlock by keeping out his 20-yard shot.
In the second half keeper Phil Barnes did well to pull down a shot come cross from Danny Sonner, and then at the other end Danny Boshell shot over the home bar.
It was not until the final minutes that the crowd had something to shout about with those efforts at either ends.
Wrexham's busy defender Carl Tremarco headed a chance wide from a Nicholson cross.
Both Managers - Wrexham's Brian Little and Grimsby's Alan Buckley - both said they were content with a point from a hard-fought game played in difficult conditions.