After three straight defeats, the Mariners produced a gritty display to ensure their losing run came to an end.
James McKeown saved a first-half penalty from Sam Smith to keep the scores level and after that, clear-cut chances were few and far between but Town were solid at the back and deserved to take something from the game.
Three changes were made to the Town side after the home defeat by Leyton Orient on Saturday, with Mattie Pollock, Elliott Whitehouse and Matt Green all coming in.
There was also a change in formation as goalkeeper McKeown was protected by a three-man central defence of Ludvig Ohman, Pollock and Luke Waterfall, with Luke Hendrie and Liam Gibson operating as wing-backs.
Whitehouse, Jake Hessenthaler and Elliott Hewitt were the midfielders, with Green alongside James Hanson in attack.