Grimsby went in front two minutes after halftime through Luke Waterfall only to see Ben Tozer and Mullin score two minutes apart to put Wrexham back in front.
The visitors equalized a second time as Ryan Taylor found the back of the net in the 72nd minute before Emmanuel Dieseruvwe gave Grimsby their first lead of the match six minutes later.
Wrexham would answer back as Jordan Davies made it 4-4 in the 80th minute and there would be no more goals until Waterfall struck in the 119th minute.
Story of the match
Grimsby thought they had taken the lead as a long throw into the penalty area by Jordan Cropper was dealt with, but McAtee's goal was disallowed after the offsides flag went up.
The hosts conitnued to have the better of the early play, Taylor heading over, but they were behind after Waterfall brought down Mullin.
The Dragons leading scorer stepped up to the spot and beat Crocombe off the underside of the crossbar.
Less than two minutes later, the Mariners were back on level terms. McAtee received the ball from 25 yards out and he blasted a drive into the top corner.
Crocombe then saved from Bryce Hosannah, tipping his low shot around the post. The ensuing corner saw a cross played in that the Grimsby shot-stopper caught easily.
The hosts thought they were back in front as Mullin latched onto a long throw from Tozer and he headed home at the far post, but the referee waved the goal off after spotting a foul.
Adam Smith headed a ball on goal, but Crocombe clawed away for a corner and he turned that aside, as well, keeping Grimsby in the match.
McAtee then fired over the bar from distance and two minutes later, his volley went just wide of the near post.
As the second half began, Clifton got down the left and played in McAtee, his shot was blocked by keeper Christian Dibble.
Seconds later, Clifton was again denied by Dibble, who dove to tip his shot away for a corner on the right. That lead to Grimsby's second as Amos’ delivery was not fully dealt with and Amos was at the back post to head home.
The visitors could have extended their lead as some neat play down the right from Gavan Holohan and Erico Sousa ended when the winger’s attempt was pushed away for a corner by Dibble.
At the other end, a first-time effort from James Jones was deflected over for a corner and Tozer headed in at the far post to make it 2-2.
Another long throw from Tozer was flicked on by Ollie Palmer to Mullin, who was on hand to bundle in.
Grimsby responded when a Sousa cross was cleared for a throw-in, then another throw from Cropper was caught by Dibble.
Ben Fox then stung the palms of Dibble with a shot from 25 yards, and that led to the Mariners equalizing for a second time. A cross from McAtee on the right was met by Taylor and his stooped header made it 3-3.
Fox won a corner on the left and after McAtee’s short delivery, a shot from Clifton was blocked. Dieseruvwe, who won Monday's elimiantor at Notts County, was left unmarked in space at the far post to nod in.
Crocombe then saved from Mullin’s powerful near-post drive, forcing a corner. That brought Wrexham's fourth, Davies rising at the far post to beat Crocombe.
Davies volleyed over the bar from 20 yards out and at the other end, Clifton had a chance to win it for Grimsby with a low strike that went wide of the far post.
Crocombe then had to tip a shot over the bar for a corner at the other end, which was headed wide by Palmer.
As the game moved into added time, a corner was met by Palmer but once again, his header went off-target.
A long throw from Cropper was then headed wide by Waterfall just before stoppage time.
Mullin drove into the box but could not pick out a teammate with his pull-back, then a penalty appeal was waved away by the referee when Davies went down.
Dieseruvwe sent a low shot through to Dibble and a cross-shot from Cropper was diverted wide by Tristan Abrahams as no further opportunities came in the first half of extra time.
The visitors had an opportunity in the 113th minute as Abrahams' shot could only hit the side-netting from a narrow angle.
But there was still drama to come as the Mariners grabbed the winner with just one minute left on the clock. A long throw from Cropper was met by Waterfall and his header beat Dibble.
The Dragons had one last chance to salvage the match as a long throw from the right by Tozer was met by Crocombe was there to claim the catch.
Man of the match: John McAtee
A stunning goal to make it 1-1 and he provided the cross for Dieseurvwe that put Grimsby ahead. Lively and confident throught, he was the Mariners best player on the day.