The game kicked off 75 minutes late after the Town team bus was held up in heavy traffic on the journey to Derbyshire but the Mariners made the better start as Hannah put them ahead on seven minutes.
Alfreton equalised through Josh Law but Hannah’s second of the game had the visitors in front at the halfway mark.
The hosts levelled matters from the penalty spot after Jon Akinde scored from the penalty spot following a foul by Shaun Pearson, then another penalty at the other end restored Grimsby’s lead and saw Hannah complete his treble.
Alfreton were not done though and after an error by Aswad Thomas, Paul Clayton capitalised to make it 3-3.
Town, backed by a magnificent following of 1,063 fans, will feel they did enough to win the game but ultimately, they were left to rue individual errors as their battle for a play-off place looks set to go down to the wire.
Four changes were made to the Town side that lost at home to Halifax in midweek, with Lenell John-Lewis, Hannah, Andi Thanoj and Paddy McLaughlin all coming into the XI.
James McKeown started in goal, with Sam Hatton, Pearson, Andrew Boyce and Thomas in defence.
Scott Neilson, Thanoj, Scott Kerr and McLaughlin were the midfielders, with Hannah and John-Lewis up front.
The Grimsby subs were Joe Colbeck, Andy Cook, Clayton McDonald, Jamal Fyfield and Oumare Tounkara.
Alfreton included former Mariners Bradley Wood and Darran Kempson in their line-up.
Despite arriving late, the Mariners made a quick start and took the lead with just seven minutes on the clock.
A through-ball found its way to HANNAH and as keeper Jon Worsnip rushed off his line, the striker prodded it past him and into the net.
It could have been 2-0 when a Kerr free kick was met by the head of John-Lewis but this time, the keeper dived to make a good save, tipping the ball around his post for a corner.
Wood was booked for a foul on Neilson as Town continued to enjoy the better of things.
But despite rarely looking threatening, the hosts got themselves back on level terms when a low cross from Daniel Meadows went to LAW, who beat McKeown from 18 yards.
Alfreton had a chance to take the lead when striker Jon Akinde took the ball inside the box and worked an opening but the Town stopper came off his line to dive and block the shot.
Boyce then conceded a corner on the left as he headed a cross behind and the kick was dealt with by McLaughlin but Alfreton worked the ball back and McKeown had to beat a powerful cross-shot away at his near post.
The game briefly stopped when John-Lewis went down injured inside the Town penalty area but he was passed fit to play on after receiving treatment.
The Mariners reclaimed their advantage on 33 minutes, when John-Lewis took advantage of a slip in the home defence to take the ball into the box before playing it across goal for HANNAH to convert at the far post.
The pendulum had swung in favour of the visitors and they won a corner through Thomas on the left but Kerr’s delivery was cleared.
A foul on John-Lewis gave Grimsby a free kick just inside the Alfreton half five minutes before half-time and from it, they should perhaps have extended their lead. Kerr’s ball was headed across goal by Pearson but Boyce could only head over the bar from eight yards.
Town were dominating now and a nice move down the left led to Hannah getting space to put a cross in from the left but it was dealt with by the home defence
The Mariners were having plenty of success down the left and a chance almost came for Thomas after the ball was flicked to him inside the box but keeper Worsnod gathered it.
A Kerr free kick was put out for a corner as the half moved into added time and from it, Town kept the ball as Alfreton failed to clear their lines. The ball came into the box from the right and Pearson headed goal wards, only to see it headed off the line as the travelling supporters at the other end of the ground were about to celebrate another goal.
That proved to be the last chance of an entertaining first half where the Mariners fully deserved their half-time advantage and could easily have been further ahead.
No changes were made before the restart and Town were first to threaten when a McLaughlin low cross led to a shot from John-Lewis being blocked for a corner three minutes in. The kick from the left was headed clear.
But the hosts were given a way back into the game when Akinde was brought down inside the box by Pearson on 51 minutes. The referee pointed to the penalty spot and after Pearson was booked, AKINDE stepped up to send McKeown the wrong way and make it 2-2.
Thomas won a Town corner on the left four minutes later but it was headed clear, before McLaughlin’s return header into the box was caught by Worsnop.
A corner at the other end was headed clear by McLaughlin and Meadows’ return cross sailed out for a goal kick.
The hosts created an opportunity to take the lead for the first time in the game when a good move saw Akinde find Paul Clayton and he touched the ball on for Law to volley over the bar.
The first substitution came just before the hour and saw Tom Shaw replace Meadows for Alfreton.
John-Lewis tried a shot soon afterwards that was deflected away for a corner on the right but it was headed away and the home side broke, although Michael hoganson was caught offside.
Neilso was the next to go close for the away side after cutting in from the right and working an opening on the edge of the box. His shot was also deflected over the bar for a corner.
A Town penalty appeal came when the travelling fans thought Wood had handballed inside his own box but the claims were waved away as Alfreton cleared.
Seconds later, a long ball from McKeown fell for Hannah but his volley was straight at Worsnop.
A foul on Hannah by Kempson, who was already on a yellow card, brought another free kick midway inside the home half but Hatton’s shot flew just over the bar after the former Town centre-back escaped a second booking.
The visitors were dominating again and a free kick from Hatton on halfway almost led to their third goal but Pearson’s header came back off the bar.
They were given a better chance to score on 70 minutes when Pearson showed good footwork inside the box until he was brought down by Kempson. A second penalty of the game was given and HANNAH confidently buried it into the net to complete his hat-trick.
The goal sparked scenes of joy among the 1,000-plus Town fans massed behind that goal, who celebrated with the players after Hannah rushed towards them.
Town were still on top as they went looking for more goals and a shot from John-Lewis was blocked for a corner on 75 minutes. Kerr’s delivery from the left was clawed away by Worsnop.
It could have been 4-2 when a cross from Neilson found McLaughlin at the far post but the ball seemed to bobble in front of him and he could only knock it over the bar.
Hatton fired a low shot that went through to Worsnop with 13 minutes to go, before McKeown was called into action for the first time in a while to push a low Shaw shot away from his goal.
Town looked in control of the game but they gifted their hosts an equaliser when a poor backward header from Thomas was seized upon by CLAYTON, who prodded past McKeown first time with 10 minutes to go.
Cook was sent on immediately after the goal, with John-Lewis the man to make way in what was a straight swap up front.
Hatton was lucky to get away with a handball on the edge of his own box soon afterwards as the home side suddenly started to believe they could claim maximum points.
But the Mariners continued to attack and they won another corner on 82 minutes, which led to Pearson heading off-target.
Akinde almost put Alfreton ahead two minutes later when he burst into the box but he could only prod his shot narrowly wide.
Hannah was flagged offside as he volleyed at Worsnop, then an Alfreton corner on the left came to nothing when Kempson could not connect with a header.
A foul on Cook 25 yards from goal gave the Mariners a free kick with two minutes to go but Hatton’s shot hit the home wall.
Shaun Harrad replaced Clayton for Alfreton, before a great block by Thomas on the line stopped a shot from Akinde from finding the net.
Four added minutes were signalled as both sides kept pushing for a winner and Thanoj had a shot blocked after good work by Cook.
But ultimately, the game ended all square, in what was a terrific advert for Conference football for the watching BT Sport viewers but perhaps a chance missed for Town to all but secure their play-off place.
The Mariners are next in action at home to Hyde on Monday.