they were held to a goalless draw by Evo-Stik Premier Division side Buxton at Blundell Park.
On a frustrating afternoon in Cleethorpes, the Mariners were unable to break down their Derbyshire opponents, who defended in numbers and grew in confidence as the game went on.
Town came into the game as the bookmakers’ favourites to win the competition and as the top side in the Blue Square Bet Premier.
But in a low-key game, any hopes the small home crowd had of a comfortable victory faded as the Mariners struggled to create many real chances.
And they may think themselves lucky to still be in the competition as the visitors missed opportunities in the later stages of the game to turn their deserved draw into a surprise victory.
Keeper Greg Fleming was handed his first start for the Mariners in place of James McKeown, as bosses Rob Scott and Paul Hurst made three changes to the side that beat Braintree last time out.
The other alterations saw Ian Miller come in for the suspended Nathan Pond, while Derek Niven replaced Ross Hannah, who dropped to the bench as the managers opted to start with a 4-3-3 formation.
Fleming began behind a defence of Sam Hatton, Shaun Pearson, Miller and Aswad Thomas, while Niven was joined in midfield by AndI Thanoj and Craig Disley.
That left Marcus Marshall and Scott Neilson to push forward from their usual wing roles to line up either side of striker Andy Cook.
Hannah was named among the substitutes, along with fellow strikers Greg Pearson, Dayle Southwell and new loan signing Michael Rankine. Bradley Wood completed the squad.
Buxton were competing at this stage of the competition for the first time in 23 years, having battled through three qualification rounds to earn their place in the first round proper.
The Bucks would be looking to forward Marc Reed to add to his nine-goal tally and inspire a famous win for the Derbyshire side.
Grimsby’s first attack came on three minutes and saw Disley run through the middle but his pass was too far ahead of Thanoj and the ball ran through for visiting keeper Ian Deakin to collect.
A foul by Disley on Kieron Lugsden gave the visitors a chance to get the ball into the Town penalty area but former Lincoln left-back Kevin Sandwith’s delivery was flicked over the bar for a goal kick.
The home side then began to take control of the game, moving the ball around inside the Buxton half and looking to create problems for Deakin.
A through-ball from Thanoj found Neilson 30 yards out on nine minutes and the Crawley loanee fired a shot but he looked to be slightly off-balance and the ball sailed into the Osmond Stand.
Thanoj drilled a low shot wide five minutes later, before a cross from Marshall was met by Cook but the referee’s whistle blew for a push against the striker as he headed at Deakin.
The visitors almost snatched the lead when a long throw from Marc Roberts was sent back across goal but striker Reed could not get enough on his header to beat Fleming.
Reed then missed the target with a long-range shot, before Cook showed good persistence at the other end to get through the Buxton backline on the edge of the box and get a shot in, although it was stopped by the keeper from a narrow angle.
Buxton winger Scott Maxfield picked up the first yellow card of the game for a foul on Disley on the Town right just after the midway point of the half.
Another long throw from Roberts was headed down for Lugsden to hook a shot over the bar from 20 yards, then a cross from Thomas on the Town left was taken by Deakin.
Town were inches away from opening the scoring on 28 minutes, when a quick break was launched after the ball ricocheted to Thanoj. He found Neilson, who slipped the ball to Cook inside the box but the striker’s drive from 15 yards crashed against the near post and bounced to safety.
Both teams were attacking in search of the first goal and a Buxton corner soon afterwards was met by Roberts but cleared by the Mariners.
A shot from Cook on the turn was deflected wide for a corner and although the kick from Neilson was cleared, Town kept possession until Hatton was adjudged to have fouled his man as he chased a Thanoj through-ball.
Town were dominating possession but struggling to break down a stubborn Buxton defence, with the visitors getting men behind the ball and looking for counter-attacks.
A Neilson cross from the right was headed away for a corner on 38 minutes but the referee blew for a foul on keeper Deakin after he appeared to drop the ball from Neilson’s delivery.
Miller then lost out to Reed on the halfway line two minutes before the break and the Bucks’ leading scorer advanced towards the penalty area before playing the ball to Michael Towey, who sliced his shot wide.
A foul on Disley gave Hatton a chance to try his luck from a free kick 25 yards out as the game moved into one added minute at the end of the half. The right-back could not break the deadlock though, as his shot went high and wide.
That proved to be the last chance of a half which had been dominated by the hosts in terms of possession, although the Town management would have wanted their side to create far more problems for the Buxton defence than they had done so far.
No changes were made by either side before the restart and Grimsby had thr first chance of the second half, with Cook glancing a header wide at the near post after a cross from Neilson on the right.
Neilson then met a Marshall cross with a diving header but Deakin got down to make the save.
Fleming had to be at his best to keep the visitors out when a Roberts long throw from the right was flicked into the path of a Buxton attacker but the keeper managed to get a hand to it, before the rebound was blocked and the ball was eventually scrambled away.
Marshall was the first Town player to be booked, seeing the referee’s yellow card after a late challenge inside the Buxton half.
The Town bosses had resisted the temptation to make changes at half-time but they acted on 53 minutes, sending Hannah on in place of Niven and reverting to a 4-4-2 formation, with Marshall and Neilson going wide and Hannah joining Cook up front.
Buxton also made a substitution soon afterwards, with Ssam Duncum replacing Morris in attack.
The away side won a corner on 57 minutes but Sandwith’s right-wing ball was punched clear of danger by Fleming.
Thomas won a corner at the other end two minutes later and it was half-cleared twice, before the danger ended when Marshall sent a wild overhead kick a long way over the bar.
Pearson was booked for a foul on the halfway line on the hour, giving Buxton, who were growing in confidence, another chance to get the ball into the box. It was headed on by Roberts into the path of Reed, who was flagged offside and appeared to pick up an injury at the same time.
Rankine replaced Cook for Town, with Neil Stevens coming on for Reed for the away side.
The Aldershot loanee’s first contribution was a powerful run into the box which brought a corner. It did not lead to a goalscoring opportunity though, with Buxton bringing the ball clear in a move that ended with Duncum curling a shot wide.
David Haggerty was the third and final Buxton substitute, replacing Kallum Keane at centre-back.
Rankine did well on the edge of the Buxton box to craft an opening, before hitting a low shot that went through to Deakin.
A high free kick from Sandwith into the Town penalty area had to be dealt with by Pearson at the expense of a corner and the Mariners were lucky not to go behind when Towey’s header from it hit the post.
Town got the ball away for another corner and it led to Thomas conceding a third flag-kick in quick succession, although this time, Pearson was able to clear.
The visitors were now creating the better opportunities, although Rankine hit another low shot on 75 minutes, which was saved by the keeper.
Marshall made way for Southwell soon afterwards as Town made their final change, with the score still goalless.
A handball gave Town a free kick in a central position with 10 minutes to go but Neilson’s 30-yard shot was pushed out for a corner by Deakin. That led to Rankine looping a shot towards the far post but again, the keeper was equal to it.
A low shot from Thanoj was also gathered by Deeakin as the clock ticked down, with the Mariners still unable to cause any serious problems and a replay beginning to loom.
Stevve Istead was booked for a foul on Hannah inside the Town half on 89 minutes and hatton’s free kick was punched away for a corner by Deakin but again, the mariners could not profit.
Five added minutes were signalled and Buxton attacked again in search of a late winner. They won a corner on the right but it was cleared by Southwell.
Thomas sliced a shot wide from 20 yards as Town kept looking for a late winner but it was not forthcoming, meaning the teams must do it all again at Silverlands.
The replay will be at Buxton on Wednesday night (7.45pm).
Grimsby Town: Fleming, Hatton, Thomas, Niven, Pearson -S, Miller, Disley, Cook, Thanoj, Neilson, Marshall.
Subs: Pearson - G, Wood, Southwell, Hannah, Rankine.
Buxton: Deakin, Sandwith, Black, Istead, Keane, Roberts, Lungsden, Towey, Reed, Morris, Maxfield.
Subs: Duncum, Haggerty, Thornhill, Bradbury, Stevens.