A single goal from Alex Rodman ultimately proved enough in what was a tight game in the West Midlands.
Rodman struck in the early stages of the game and after that, genuine chances for the Mariners were few and far between.
Nuneaton stepped things up after the break and pressed hard for an equaliser but the Town defence held on to move back into the Skrill Premier’s top five.
Lenell John-Lewis came back into the Town side after being rested for Tuesday’s defeat by Forest Green Rovers.
His inclusion was one of three changes to the line-up, with Paul Bignot and Rodman also coming in.
James McKeown started in goal, with Bignot, Shaun Pearson, Andrew Boyce and Aswad Thomas forming the defence.
Rodman, Craig Disley, Scott Kerr and Scott Neilson were the midfielders, with John-Lewis and Connor Jennings picked as the attackers.
The Town subs were Cook, Clayton McDonald, Ross Hannah, Andi Thanoj and Oumare Tounkara.
Nuneaton were playing their first game since losing manager Kevin Wilkin to Wrexham in midweek, with injured player Simon Forsdick taking charge for the afternoon.
A foul on John-Lewis gave Town their first opportunity to get the ball into the home penalty area but Kerr’s free kick was cleared.
The Mariners took the lead on seven minutes with their first good chance of the game, when a good cross from Thomas on the left fell for RODMAN at the far post and he volleyed emphatically past keeper James Belshaw.
Town had controlled the early stages of the game but the hosts won the first corner on 12 minutes. Daniel Sleath’s delivery curled in towards McKeown, who had to push the ball clear.
Both sides were looking to use a direct approach, with Grimsby pumping long balls forward towards John-Lewis and Nuneaton struggling to put together any spells of possession.
Another home corner came after striker David Hibbert had controlled the ball inside the Town box but again, the ball from the flag was comfortably dealt with.
Right-back Sam Magri dispossessed Neilson near the halfway line soon afterwards and sent a cross in from the Nuneaton right but striker Andy Brown could not get a strong enough connection on it to trouble McKeown.
John-Lewis was shown the first yellow card of the game on 25 minutes after a foul deep inside the home half of the field.
Brown had the next half-chance for the hosts when left-back Theo Streete crossed towards the far post but again, the header went harmlessly through to McKeown.
Jennings won Town’s first corner on the half-hour but the referee’s whistle blew for an infringement as Kerr’s ball landed on the roof of the net.
Hibbert had a chance to equalise after a cross from Wes York came off Boyce and fell for the striker but his volley was kept out by McKeown at the expense of a corner.
A period of Town possession then came, with a number of throw-ins down the left side, albeit without any problems being caused for the home defence.
Pearson conceded a free kick on the Nuneaton right two minutes before the break but Sleath’s delivery was poor and Gavin Cowan was penalised for a foul as it came across, with the defender shown a yellow card.
Thomas then had to give away a corner in added time but the left-wing delivery was comfortable for the Town keeper.
Overall, it had been a first half low on incidents, with both sides looking to play long balls and get the ball to the strikers as quickly as possible.
The home side had caused very few problems and Town would have been pleased to go in with the lead at the interval, although they would be looking to step up the tempo and kill the game off after the break.
No changes were made before the restart and the Mariners had the first chance of the second half when Kerr sent an effort wide from 20 yards.
A long ball from Streete proved just too far ahead of York for him to connect, before a Nuneaton free kick from the right looked like causing problems but was eventually dealt with by the Town defence.
McKeown was called into action to preserve Grimsby’s lead with a double save on 54 minutes, with Hibbert denied as he attempted to bring Nuneaton level.
The hosts, after showing little threat throughout, had started to play the ball along the ground and were getting some joy down the left.
Pearson became the second Town player to be booked, before McDonald came on for Bignot, who had picked up an injury, as the visitors made the first substitution.
A low John-Lewis cross was cut out for a corner and after Kerr’s delivery was missed by keeper Belshaw, nobody in black and white was there to convert amid confusion in the home defence.
Louis Moult replaced Magri for Nuneaton and they should have been level on 62 minutes when a cross from the right found York unmarked but his shot went across goal and missed the target.
Good skill by John-Lewis at the other end led to an opening for Town but the striker’s shot was blocked.
Nuneaton were controlling the game though, getting forward and looking more dangerous as the game went on.
The hosts were almost gifted an equaliser when a back-pass from Neilson fell very short and Streete nipped in but McKeown raced off his line and did enough to put off the attacker, who fired wide.
A run by Thomas down the left ended with the full-back winning a corner and after Thanoj replaced Neilson, Kerr’s delivery was headed at Belshaw by Boyce at the far post.
Moult missed his kick when he looked poised to volley the home side level after a chipped cross from the left on 77 minutes, meaning Town’s lead remained intact.
A cross-shot from Streete then came a minute later but McKeown was equal to it, getting down to make the save.
Adam Walker hit a wild shot well off-target from long range with nine minutes to go as the home side kept looking for a way back into the game.
Disley was booked for a foul near the centre circle but again, Town were able to hold firm from the free kick, with an overhead kick attempt blocked. The ball then bounced around in the penalty area as the Mariners had all 11 men back, before they eventually got the ball away.
Tounkara, who was warming up on the touchline, was shown a yellow card for kicking the ball away after it went out for a throw-in.
Former Town striker Greg Pearson replaced Hibbert up front for Nuneaton for the last five minutes, before Brown sent a free header over the bar as the hosts continued to create chances.
A home corner came on the left a minute from time but McDonald headed it clear for a throw-in. From it, the pressure continued and McKeown punched a cross away, before another centre went out for a goal kick.
Cook replaced John-Lewis for Town as the game moved into five minutes of stoppage time.
And Town again held firm throughout the added time to secure an important three points.
They are next in action when league leaders Luton Town visit Blundell Park on Tuesday.