Defender Ben Cuff had given the visitors the lead early in the game but the young Town defender was in the wrong place to deflect a Kyle Dixon cross into his net before Romello Nangle snatched the win for the Magpies with 14 minutes remaining.
Adam Smith's side pushed for an equaliser but Blaize Kerr saw a fantastic, dipping volley from fully 30 yards come crashing back off the crossbar.
Town stopper Harry Ashton was the first to be called into action on eight minutes when he safely gathered Glodie Bange's shot from distance.
But then the young Mariners found their feet. Caine Winfarrah teased his marker and whipped in a teasing cross that Brad McGowan could only hook towards his own goal where Kyle Simmones was on hand to mop up the danger.
There was no such let-off for the Magpies on the quarter-hour though. Josh Morrall did well to work some space on the left and, although his cross was partially cleared, centre-half Cuff was on hand to hammer home a half-volley from 15 yards.
County responded well with Kameron Campbell swinging in corner that was met by McGowan but Ashton was equal to the effort.
And then the Mariners' top scorer Robbie Bryant came tantalisingly close to putting Town two to the good. The striker robbed Matty Crust in the midfield and curled a fantastic effort towards the top corner, only for Harry Andrews to pull off a fantastic fingertip save.
Ashton was called upon to deny Dixon and then Elliot Hodge as the game moved past the half hour before Bange fired wide when played through by Nangle.
The young Mariners went into the break with a slender advantage but unfortunately that lead was to last just three minutes into the second period as the hosts drew level.
Dixon and Campbell worked a short corner on the right and the ball into the box was diverted past Ashton by the unfortunate Cuff.
Now the visitors were under pressure and Kieran Kenlock was inches from edging County in front with a powerful 20-yard drive after cutting in from the left.
Big defender Kieran Geldenhuys flashed a header just wide of the target before Bange was left banging the ground in frustration after he fired straight at Ashton when clean through.
Smith responded by throwing young Paul Walker into the mix and his first action of the game saw him cross for Bryant, who nodded agonisingly wide at the far post.
Bange again sprung the offside trap on 70 minutes but this time the County livewire hammered his effort into the stands with just Ashton to beat.
But with 14 minutes to go the home side's pressure paid off and they edged in front.
Nangle picked up the ball in midfield and arrowed a low drive into the bottom corner from distance.
The Town youngsters didn't let their heads drop and less than 60 seconds later Bryant was again ruing the intervention of home stopper Andrews.
It was another header from Grimsby's 17-goal frontman but Andrews arched back to tip the ball over the crossbar when a goal looked certain.
And still the visitors pushed for an equaliser and it nearly came from the unlikely boot of another defender, Blaize Kerr. The young full back pushed forward and unleashed a tremendous volley that dipped and swerved and had Andrews beaten all ends up but hit the bar and was cleared.
The home side managed to see out the game in the closing moments and they now are guaranteed of top place in the group after winning both their games - having earlier beaten Mansfield Town at the One Call Stadium.
The Mariners have their rearranged tie with the Stags to come.
County: Andrews, Campbell, Simmones, Crust, McGowan, Geldenhuys, Kenlock (Lavelle-Moore 72), Hodge, Bange (Randall 84), Dixon (Guest 88), Nangle. Subs not used: Clarke, Guy
Mariners: Ashton; Kerr, Morrall, Humble, Cuff; Smith, Wattam, Griffin, Peers, Winfarrah (Walker 65); Bryant. Subs not used: Loughran, Robinson, Charlesworth, Falconer