In a game of few chances for either side, one goal was enough to win it, as substitute Omari Patrick's strike on 78 minutes proved decisive.
Charles Vernam replaced Harry Clifton in the only change to the Town starting XI following last week's defeat by Newport County.
New signing Elliot Embleton was handed a place on the bench after completing his loan move from Sunderland on Thursday, although Ben Pringle's signing came too late for him to be involved.
James McKeown started in goal, with Luke Hendrie, Harry Davis, Alex Whitmore and Akin Famewo forming the defence.
Martyn Woolford, John Welsh, Jake Hessenthaler and JJ Hooper were the midfielders, with Vernam and Jordan Cook in attack.
Embleton and Clifton were joined on the bench by Mitch Rose, Louis Robles, Andrew Fox, Max Wright and Sam Russell.
Yeovil's line-up included Diallang Jaiyesimi, who made his first return to Blundell Park after spending last season on loan with the Mariners.
An early free kick brought a first opportunity for Town to get the ball into the danger zone but Hessenthaler's delivery beat everybody and went out for a goal kick.
Woolford sent a cross over from the right on five minutes but Hooper was unable to fully connect with a header to turn it towards goal.
Yeovil's first attempt cme through striker Alex Fisher, who tried his luck from 40 yards after spotting McKeown off his line but missed the target.
The game's first corner came at the other end soon afterwards and the visitors failed to fully clear despite captain Omar Sowunmi being first to Hessenthaler's delivery. The pressure was relieved though after a foul brought a free kick.
Good play by Hooper led to a chance for Vernam on 12 minutes, although his shot from 20 yaards was pushed wide for a corner by visiting keeper Nathan Baxter, who caught Whitmore's header from the flag-kick.
Vernam saw a shot blocked for another corner as the hosts continued to dominate the early stages. This time, Baxter punched clear.
A chance for Yeovil came on 15 minutes after persistence from Jaiyesimi saw him work an opening for a shot but it was blocked by Whitmore for a corner.
Midfielder Sessi D'Almeida was shown the first yellow card of the game for a foul on Hendrie after the referee had initially allowed a good advantage.
Davis did well to deny Jordan Green after the pacy winger had set off on a run through the middle following a quick counter-attack, with Jaiyesimi eventually shooting wide.
An attempted cross by Bevis Mugabe was blocked for a corner by Famewo on the half-hour and after the Mariners failed to fully clear their lines, Jaiyesimi won another corner.
A third flag-kick in quick succession followed after Town again failed to clear, although this time, McKeown claimed a catch.
Vernam had a shot blocked for a corner on the left on 35 minutes but Hessenthaler's delivery was poor, hitting the side-netting.
Gary Warren was penalised for a foul on Cook inside the Yeovil half five minutes later and after Hessenthaler's free kick was headed away, the ball eventually came back to him an he sent a curling shot over the bar.
After a bright opening 15 minutes by the Mariners, the away side had grown into the contest but neither goalkeeper had been particularly busy over the course of the half.
A good ball from Vernam on the left brought a shooting opportunity for Hendrie three minutes before the break but he missed the target from 25 yards.
One added minute was signalled to be played at the end of the half and a Yeovil corner came when an effot from Alex Pattison was blocked. The ball from the flag was headed clear, meaning it remained goalless at the interval.
No changes were made before the restart and Jaiyesimi was denied by Davis as he looked to work an opening inside the penalty area five minutes in.
Yeovil made the first substitution on 56 minutes, as Green was replaced by Olufela Olomola, making his first appearance since returning to the club on loan from Scunthorpe United.
Cook steered a header wide of the near post in Town's first opportunity of the half, before Hendrie had to concede a corner at the other end, which he also headed clear.
Fox replaced Hooper in Grimsby's first change of the game, then a deflected effort by Woolford bounced through to Baxter.
Cook was booked for an infringement on the edge of the Yeovil box, before the second home substitution saw Clifton come on in place of Woolford.
Jaiyesimi went off to be replaced by Patrick, with chances still few and far between for both sides.
A low shot by Vernam from 20 yards was deflected away for a corner on the right but Hessenthaler's ball was headed clear before it could reach Whitmore at the far post.
A corner then came at the other end on 76 minutes but it did not lead to a chance in front of goal.
Two minutes later though, the visitors made a breakthrough when PATRICK did well to control the ball, work an opening and curl a low shot beyond McKeown and into the far corner of the net.
Town had been set to bring Embleton on for his debut but the goal meant it was instead Mitch Rose who came on in place of Davis. Jake Gray replaced Fisher in the Yeovil attack at the same time.
The Mariners were looking for a way back into the game and they almost had it when Cook met Clifton's right-wing cross but seent hi header over the bar.
Patrick then had a great chance to seal the points for Yeovil but shot wide from inside the box.
Town were given an additional four minutes to search for an equaliser but they were unable to find it as Yeovil secured the points.
The Mariners are next in action on Tuesday, when Notts County visit Blundell Park in the opening Checkatrade Trophy group match.
1 James McKeown
24 Harry Davis
27 Luke Hendrie
25 Alex Whitmore
12 Akin Famewo
4 John Welsh (C)
18 Charles Vernam
7 Jake Hessenthaler
11 Jordan Cook
16 Martyn Woolford
9 JJ Hooper
23 Sam Russell
19 Andrew Fox
15 Harry Clifton
22 Elliot Embleton
8 Mitch Rose
20 Max Wright
14 Louis Robles
12 Nathan Baxter
5 Bevis Mugabi
3 Carl Dickinson
6 Omar Sowunmi (C)
4 Gary Warren
17 Alex Pattison
18 Yoann Arquin
20 Sessi D'Almeida
11 Jordan Green
14 Diallang Jaiyesimi
25 Stephen Phillips
10 Jake Gray
15 Gabriel Rogers
30 Alefe Santos
19 Korrey Henry
24 Olufela Olomola
8 Omari Patrick
Attendance: 4284 (72)
Referee: Thomas Bramall