In a game of few chances, Town were forced to play most of the second half a man down after Joe Colbeck was sent off for retaliating after he was fouled.
The Mariners had opportunities to win the game, with Lenell John-Lewis having a chance to break the deadlock just before half-time.
But ultimately, they were forced to settle for a point, despite remaining relatively untroubled by the home attack.
Four changes were made to the Town side that lost heavily at Halifax in midweek, with Alex Rodman, Andi Thanoj, Clayton McDonald and Scott Neilson all dropping out of the starting XI.
They were replaced by Ross Hannah, Ritchie Jones, Chris Doig and Colbeck, with Liam Hearn and Aswad Thomas both returning to the squad on the substitutes’ bench.
James McKeown continued in goal, with Paul Bignot, Shaun Pearson, Doig and Alan Goodall forming the defence.
A change of system meant there was a four-man midfield of Colbeck, Scott Kerr, Jones and Patrick McLaughlin, while Hannah was partnered with John-Lewis in attack.
Neilson and McDonald dropped to the bench, alongside Thomas, Hearn and Andy Cook.
Chester had the first chance to create some danger with a long throw into the box but a foul on Kerr by Danny Higginbotham gave the Mariners a free kick.
Soon afterwards, striker Gareth Seddon was put through but could not capitalise, taking himself wide before hitting a shot which did not trouble McKeown.
Grimsby’s first chance of the game came on nine minutes, when John-Lewis hit a long-range shot that went just past the post.
Town then won a corner on the left, which was drilled across by McLaughlin for Hannah to shoot at home keeper John Danby.
A late challenge on Kerr gave Town a free kick on 16 minutes and it led to another corner, which was half-cleared before a shot from Kerr was blocked.
A foul by Pearson gave the home side a free kick four minutes later and from it, the former Boston centre-back got to the ball first to head it away for a corner.
That led to another flag-kick, which was again dealt with by the Town defence, before a shot by Aidan Chippendale went wide as the Chester pressure continued.
Chippendale almost had another opportunity when he beat the Town offside trap to meet a long ball through the middle but his touch took it through to McKeown.
A Colbeck cross was blocked after a Town move down the right on 28 minutes, before Bignot became the first to be shown a yellow card four minutes later.
Striker Ben Mills then went down inside the Grimsby penalty area under a challenge but the home penalty appeals were waved away.
Few chances were being created by either side as half-time began to loom, although some persistent play by Hannah saw John-Lewis presented with an opportunity on 41 minutes but his shot from close range was deflected by keeper Danby and then headed clear off the line.
Another shot, this time by Kerr, came after Colbeck had combined with Hannah but the midfielder’s effort flew over the bar.
Two added minutes were played at the end of the half and with no further opportunities for either side, the game remained goalless at the break.
After the restart, an early free kick by Chippendale was cleared and Town broke, with Hannah sending a ball through to the onrushing Jones but he was penalised for a foul.
Town had started the second half brightly but they were reduced to ten men when Colbeck was dismissed for retaliating after he was fouled and the referee had no hesitation in brandishing the red card.
McKeown claimed a cross from Chippendale shortly after a long ball had been headed out for a throw-in by John-Lewis as Chester looked to make their numerical advantage tell.
John-Lewis won a free kick when he was fouled by defender Michael Kay, who was booked. Hannah’s shot from it went into the Chester wall.
Jones had a shot blocked after a spell of Town possession around the 62-minute mark, before Goodall did well to stop a break by the hosts.
A foul by Doig gave Chester a free kick on the edge of the Mariners box three minutes later but Chippendale’s delivery was cleared for a corner by Hannah.
Mills was yellow-carded for an infringement at another home corner, before he was replaced soon afterwards as Chester made the first substitution.
Town replied with a change of their own, bringing Cook on for John-Lewis with 22 minutes to go.
Hannah missed the target with a shot after Jones had won the ball but the offside flag was up against the striker in any case.
A chance for Chester came with 15 minutes to go but McKeown was equal to it, saving the shot with his legs.
Hannah was replaced by Hearn in the Grimsby attack two minutes later, before a Town free kick almost led to a shooting chance for Cook.
Another Chester substitution saw Craig Mahon come on for Chippendale with eight minutes left.
Four added minutes were signalled by the fourth official , giving both teams more time to find what would surely be the winning goal.
A Town free kick came in the second of those extra minutes but the game stopped after a clash of heads followed Goodall’s delivery into the Chester box.
No further chances came for either side, meaning they were forced to settle for a point apiece.
Town will look to build on the result when they face Dartford at Blundell Park on Tuesday