The Mariners started well and took the lead when Scott Neilson opened the scoring against his previous club.
But their advantage was short-lived, as Matt Robinson equalised for the visitors, who then grew into the game.
Both sides had chances to get the crucial third goal of the game but it was the away side who struck the decisive blow through Paul Benson on the hour.
Just one change was made to the Town side that won at Nuneaton on Saturday, with Sam Hatton coming in for the injured Paul Bignot at right-back.
Otherwise, it was as you were, with James McKeown in goal and Shaun Pearson, Andrew Boyce and Aswad Thomas completing the defence.
Saturday’s goalscorer Alex Rodman started on the right of midfield, with Craig Disley and Scott Kerr in the middle and Neilson on the left.
The attacking partnership was unchanged, with Lenell John-Lewis alongside Connor Jennings.
Ross Hannah, AndI Thanoj, Paddy McLaughlin, Jamal Fyfield and Oumare Tounkara were all named as substitutes.
Runaway league leaders Luton made the journey north looking to take another step towards automatic promotion back to the Football League with a win.
They would be looking to the experienced Benson and 26-goal leading scorer Andre Gray to hit the net again to take the points back to Bedfordshire.
Town thought they had created a goalscoring opportunity within the opening 30 seconds but John-Lewis was flagged offside as he shot wide.
A foul on the striker then brought a free kick on five minutes but Kerr’s delivery was cleared by defender Steve McNulty.
A spell of Town pressure came after Rodman charged down a clearance from Scott Griffiths and put a cross in from the right which was partially cleared. The hosts worked the ball back and won the first corner of the game, which was dealt with by the Hatters defence.
John-Lewis hit a weak shot through to keeper Mark Tyler on nine minutes as Grimsby’s promising start continued, before Alex Lawless was caught offside on the right as Luton showed their first signs of attacking threat.
A Hatton cross from the right was put behind for a corner on the quarter-hour and from it, a header from Boyce was cleared off the line by Gray before John-Lewis could only prod the rebound wide from close range.
The next chance led to the opening goal on 18 minutes, as a cross from Rodman on the right was missed by Tyler and NEILSON had the relatively simple task of firing home from 10 yards.
But Town’s lead was to last just two minutes, as they failed to clear a cross from the Luton right and ROBINSON eventually stepped in to beat McKeown and put the ball into the net.
The home side’s response saw Rodman hot a shot from 20 yards that Tyler got down to stop.
Luton were beginning to get into their stride and a counter-attack from them through midfielder Pelly Ruddock-Mpanzi led to a shot from Gray being blocked for a corner.
A Kerr free kick for a foul on John-Lewis was well cleared by Benson and the visitors looked to launch another attack through the middle but it was stopped by Thomas near the halfway line.
Ruddock-Mpanzi looked to play a through-ball for Gray on 32 minutes but the pass proved just too far ahead of the striker and McKeown came off his line to gather it.
A foul on Pearson on the halfway line earned Robinson the first yellow card of the night soon afterwards, with Rodman hitting a shot over the bar after Hatton’s free kick was cleared to him on the edge of the penalty area.
Gray could have given Luton the lead when he got on the end of a long pass on 37 minutes but he dragged a low shot just wide of the target from 20 yards.
A free kick for handball against Robinson gave Town a chance to get the ball into the box but Kerr’s chip was headed clear by McNulty.
McKeown was then called into action when a cross from Lawless was headed towards goal. The keeper got a strong hand to the ball, which was then cleared from danger.
At the other end, Thomas won a corner on the left three minutes before the break but Kerr’s delivery was cleared, as was a follow-up cross from Rodman.
The Mariners kept possession though and they won another corner seconds later, which was eventually scrambled away after Tyler failed to claim the ball from Kerr’s kick.
Three added minutes were played at the end of the half and Jennings almost had an opening to get a shot in early in for Town, before an attempted chip by Rodman was deflected away from goal.
Grimsby were finishing the half strongly and Tyler had to get down quickly to make a good save from Disley, whose far-post header looked like it was going to give the hosts their lead back.
That proved to be the last chance of an entertaining first half, which ended with the scores level.
No changes were made before the restart and the away side got off to a fast start when a run from halfway by Gray led to an early corner. Lawless took the kick but referee Ross Joyce blew for a Town free kick for a foul as it came over.
A foul on John-Lewis gave the Mariners their first opportunity of the half four minutes in but Hatton’s resulting free kick flew over Tyler’s bar.
Town won a corner on the left three minutes later and the ball was cleared from it, before McKeown’s return ball into the box cleared everybody and went out for a goal kick.
Another attack came soon afterwards when Jennings found Rodman on the right but his cross was caught by Tyler.
Neilson and Thomas then linked up down the left for the full-back to cross but the header from John-Lewis went wide of the target.
A good move down the left involving Neilson and Jennings led to Hatton having a shot blocked.
Luton broke away and took the lead for the first time in the game seconds later, when a low shot from Scott Griffiths bounced back off the post and BENSON reacted quickest to slam the rebound into the net in front of the travelling supporters.
Neilson and Rodman appeared to have crafted a chance for Town to hit back on 67 minutes but the home attackers were crowded out inside the box and Luton cleared.
Kerr shot just over the bar from the edge of the area a minute later, before a Luton free kick led to Lawless hitting a low shot that McKeown got down to save.
Jennings then tried a speculative long-range effort that swerved in front of Tyler, who had to push the ball away for a corner.
Tounkara replaced John-Lewis as Town made the first substitution of the game before the kick was taken and headed behind for another corner on the opposite side, which was eventually cleared.
Again, Luton broke quickly and this time, it was Ruddock-Mpanzi who went through and looked to take the ball past the onrushing McKeown before going down under a challenge from the Town keeper just outside the box. The referee took no action, ruling there had been no foul and allowing play to continue.
A free kick for the visitors did come on 73 minutes but Lawless’ chip towards the far post was headed away for a throw-in by Pearson.
Rodman drilled a shot at Tyler after good work by Tounkara soon afterwards as the Mariners looked for a route back into the game.
But they almost went further behind when Gray latched onto a through-ball and took it into the box but he lashed his shot into the side-netting at the near post.
Hannah came on for Rodman as Town boss Paul Hurst looked to freshen up his attack with 10 minutes to go.
Jennings hit a cross-shot from the right on 85 minutes but Hatton could not get a touch to it and Tyler collected the ball at his far post.
Ruddock-Mpanzi was penalised for a foul on Disley inside the Luton half but Hatton’s free kick was cleared as far as Jennings, who won a throw-in on the right.
Much of the game was being played in the Luton half, with the Mariners throwing everything forward in search of an equaliser as the game moved into four minutes of added time.
But for all their territory and attacking play, the home side were struggling to make a real impact in front of goal, as Luton dealt with everything that was thrown their way.
And that meant the visitors were able to close out their victory and move further clear at the top of the league.
Town will look to bounce back when they travel to Hereford United on Saturday.