The Mariners were looking to climb into the play-off positions by following up Saturday’s home victory over Braintree with another three points.
Instead, they found themselves three goals down in a little over half an hour, with a Dan Gardner double following Marcus Carver’s opener.
And their slim hopes of getting anything from the game disappeared when Adam Smith made it 4-0 shortly after half-time.
Town boss Paul Hurst named an unchanged starting XI after the weekend win.
That meant it was James McKeown in goal, with Paul Bignot, Shaun Pearson, Clayton McDonald and Alan Goodall across the back.
Andi Thanoj, Scott Kerr and Patrick McLaughlin were again named as the midfielders, with Alex rodman, Lenell John-Lewis and Scott Neilson continuing in attack.
There were changes amongst the substitutes though, with new signing Ritchie Jones involved for the first time after receiving international clearance to play and Chris Doig returning.
The bench was completed by Andy Cook, Ross Hannah and Joe Colbeck, meaning there was no place in the match day squad for Liam Hearn.
Halifax won the first corner on three minutes when a shot by Gardner was deflected behind but the kick caused no real problems for the Town defence.
A better chance came when a ball from Smith to the far post was met with a downward header by Scott McManus but McKeown got down to beat it away.
At the other end, home keeper Matt Glennon beat John-Lewis to a cross from McLaughlin as the Mariners looked for their first opening.
An attempt by Matty Pearson for the hosts was blocked by McDonald and the resulting throw-in almost led to another chance for the midfielder when the ball dropped to him after McKeown punched it but he could not redirect it towards goal.
Town almost created a chance after a spell of possession and build-up play down the right led to Rodman crossing but his ball went beyond McLaughlin at the far post.
Halifax took the lead on 19 minutes when Smith did well on the right to engineer an opening before crossing for CARVER to head home from close range.
Eight minutes later, it got worse for Town when the home side doubled their lead. This time, it was GARDNER who found his way into the box before hitting a deflected shot past McKeown and into the far bottom corner.
Grimsby’s response saw Rodman look to work an opening after a quick break but he was crowded out by Halifax defenders.
That proved to be only a brief respite as the hosts stretched their lead further just after the half-hour. A Town attack broke down and Smith slid a ball through for GARDNER, who saw his first shot saved by McKeown but made no mistake from the rebound.
The Mariners responded by making a double substitution ten minutes before the break, with Hannah and Jones replacing Thanoj and Neilson in an attempt to change the course of the game.
Hannah had a shot blocked before a sliding challenge from Simon Ainge prevented John-Lewis from making progress into the Halifax box as Town looked for a lifeline before half-time.
A ball from Rodman eluded Hannah, who was one of several Grimsby players in the box, soon afterwards and it was cleared for a corner, which was cleared.
From there, Halifax launched a counter-attack which saw the hosts get a three-on-two situation but Pearson was able to deal with the danger and get the ball away.
A foul on Kerr gave Town a free kick in midfield and McDonald’s delivery into the box found John-Lewis but his header was caught by Glennon.
Two added minutes were played at the end of the half and John-Lewis was blocked for a Town corner, which led to Rodman striking a shot that hit Hannah.
That proved to be the last chance of the half, meaning the Mariners went into the dressing rooms with a three-goal deficit to make up.
No further changes were made before the restart and Town were further behind just two minutes in, when Jones lost possession in midfield and the ball was played to SMITH, who drove forward from the right and smashed a shot into the net off the post.
Town had an opportunity to pull one back on 51 minutes when John-Lewis was fouled on the edge of the box but Jones fired the free kick wide.
Hannah scooped a long-range shot over the bar soon afterwards, before another Halifax attack led to a free kick for a foul by McDonald, who then headed McManus’ delivery away.
McDonald was booked for a foul on Smith just before the hour but the low free kick went through to McKeown in the Town goal.
Soon afterwards, Gardner was inches away from completing his hat-trick when he chased a ball down and smashed a shot across goal that hit the post.
Centre-back Marc Roberts headed over from a corner as the hosts continued to dominate, before Smith fired wide from long range.
Colbeck replaced Rodman for Grimsby on 63 minutes and Hannah had a chance to pull a goal back soon afterwards with a left-footed shot but keeper Glennon was equal to it.
Hannah won a free kick three minutes later but it did not cause any problems for Glennon, as Goodall eventually sent his shot into the terracing behind the goal.
Jordan Ball and John McReady came on for Halifax with 20 minutes to go, just before a whipped cross from Colbeck just eluded John-Lewis and McLaughlin.
A volley from McLaughlin was well off-target soon afterwards, before Bignot blocked a cross at the other end at the expense of a corner, which led to McKeown saving from Roberts.
Sean Williams replaced Gardner for the home side on 76 minutes as they looked to extend their advantage.
But it was the Mariners who had the next chance, with Colbeck crossing for Hannah, whose shot was saved by Glennon.
Former Halifax loanee Hannah was again thwarted by the Shaymen keeper four minutes from time, before Ball hit a shot wide for the hosts.
Halifax had a chance to make it five with a late free kick but the ball was curled over the bar, although the damage had already been done.
Town will look to get back on track when they travel to Chester on Saturday.