In a tight game with few chances for either side, one goal proved enough as midfielder Lois Maynard struck seven minutes after half-time.
Town had missed their best opportunity of the game through Oumare Tounkara in the first half and they were unable to respond after going behind.
The result meant the Mariners were overtaken in the league table by their visitors from West Yorkshire, although results elsewhere meant they remain four points clear of sixth-placed Braintree in the battle for the all-important play-off places.
Three changes were made to the Town side that beat Chester on Saturday, as striker Andy Cook was rewarded for his goalscoring substitute appearance with a start.
He replaced Connor Jennings, while Aswad Thomas made a return from injury to start at left-back and Joe Colbeck came in for Alex Rodman on the right side of midfield.
James McKeown began in goal, with Sam Hatton, Shaun Pearson, Andrew Boyce and Thomas forming the defence.
Colbeck, Craig Disley, Scott Kerr and Scott Neilson were the midfielders, with Tounkara selected alongside Cook in attack.
The Grimsby substitutes were Clayton McDonald, Ross Hannah, Andi Thanoj, Paddy McLaughlin and Jamal Fyfield.
Halifax were looking to continue an excellent run of form that had seen them join the Mariners in the Skrill Premier’s play-off zone.
Neil Aspin’s side had won each of their previous four away games, scoring 11 times and conceding only once in that time.
Their main attacking threat was likely to come from Lee Gregory, who was out to add to his tally of 28 goals so far this season.
An early free kick to the visitors was pumped into the Town box by Danny Lowe but it was dealt with by the home defence.
Grimsby’s first opening then came when a deep cross from Hatton was met by Cook but his header went over the bar for a goal kick.
Boyce had to concede a throw-in on the left on seven minutes, giving Marc Roberts a chance to utilise his long throw. Cook dealt with the danger though, heading the ball clear.
Town were struggling to keep the ball on the ground in the early stages, with aerial balls the order of the day in the opening 10 minutes.
Matty Pearson missed the target with a shot from 25 yards for the visitors, before defender Chris Smith picked up the first yellow card for bringing Disley down after the midfielder had pushed the ball past him.
Tounkara had a great chance to put the Mariners ahead on the quarter-hour when he took advantage of a slip in the Halifax defence to leave himself one-on-one with keeper Matty Glennon. The stopper did well though, racing off his line to narrow the angle and make the block.
McKeown was called into action for the first time moments later to stop a shot from the edge of the box but he too did well, diving to keep the ball out and preventing a corner.
Thomas and Neilson linked up down the left to get the hosts into an attacking position on 21 minutes but the winger lost the ball.
A minute later, Tounkara found Colbeck on the right and he won the game’s first corner, which led to Pearson heading over the bar.
Town were starting to play more football as the half-hour approached and they won another corner when a low cross from Thomas was sliced out. Kerr’s kick was caught by Glennon.
Thomas won another corner on the left on 31 minutes but the result was the same, as the keeper came off his line to claim the catch.
Halifax had not looked threatening but they were given a chance when a foul by Pearson brought about a free kick in a central position, 25 yards out. The shot hit the Town wall.
Another free kick came seconds later for a foul by Thomas, who was booked. This time, the delivery from the right was headed out for a throw, which caused no problems for the Grimsby defence.
A spell of Town pressure followed, with the game in the Halifax half until a ball from Kerr was headed away by Roberts.
Lois Maynard was yellow-carded for a foul on Colbeck on 37 minutes but Kerr’s floated ball towards the far post went out for a goal kick.
Another free kick, this time for Halifax, came a minute later but Paul Marshall’s delivery also evaded everybody and went out for a goal kick.
The referee’s yellow card was out again two minutes before the break when Kerr was penalised for a late challenge on Halifax’s Pearson.
Neilson had a shot soon afterwards after receiving a pass from Disley but the effort did not trouble Glennon, who watched it go over his bar.
One added minute was played at the end of the half and with no further chances for either side, it remained all-square at the interval.
The teams had mostly cancelled each other out, with few genuine opportunities created by two well-matched sides.
No substitutions were made before the restart and Town were the first to attack in the second half, as Tounkara pushed a shot wide of the near post from the right side of the penalty area.
Good work by Tounkara on 49 minutes led to Colbeck having a shooting chance but his 20-yarder was too high.
Halifax had their first chance of the half three minutes later and from it, they took the lead. A quick free kick from the right was worked to MAYNARD and he cut in and curled a left-footed strike that beat McKeown and found the top corner of his net.
Gregory was fouled as he looked to get past Pearson on the halfway line and after the free kick was played towards the 18-yard line, the striker had a shot blocked.
Cook looked to have been given an opening when strike-partner Tounkara laid the ball off to him but the former Barrow man could not capitalise and he was crowded out by away defenders, before heading over the bar soon afterwards from a Hatton cross.
Gregory had been quiet for most of the game but he did well to hold the ball up inside the Town box on 65 minutes before playing it to Scott McManus, who drilled a shot wide from 20 yards.
A Colbeck cross was cut out as the Mariners tried to find an equaliser, before a double substitution saw Hannah and McLaughlin replace Tounkara and Colbeck.
Gregory won a corner when his cross was deflected behind on 72 minutes but Marshall’s low delivery was cleared by McLaughlin.
Roberts was the next to be booked for a foul on Hannah and before the free kick was taken, Halifax replaced Scott Spencer with Ryan Crowther.
Town won a corner when a Thomas cross from the left was blocked but again, they were unable to make it count as the ball was caught by Glennon.
Gregory tried a speculative shot from 30 yards as the game approached its last 10 minutes but the attempt never looked like causing any problems as it sailed over the bar.
The visitors were looking the better of the two sides and they won another corner on the right, which was blocked.
Thanoj came on for Kerr with a little over eight minutes left to play.
Town kept pushing for an equaliser and McLaughlin hit a shot that just missed the target from 18 yards on 88 minutes.
Four added minutes gave the home side more time to rescue a point and they spent it camped in the Halifax half.
A free kick on the left gave them one last chance to snatch a draw but Hatton’s whipped delivery beat everybody and landed on the roof of the net at the far post.
That proved to be the last chance of the game, leaving the 400-plus travelling supporters to celebrate their fifth straight win on the road.
Town remain in a good position to secure a play-off place though and they will look to further cement their position in the top five when they travel to Alfreton Town on Friday.