The Glovers fell behind with just seven minutes on the clock courtesy of Sam Jones’ penalty from what was the hosts first meaningful attack.
In a first period lacking in chances, the Mariners doubled their lead 10 minutes before the break when Chris Clements found the net to leave Town reflecting on a half of frustration.
If the first-half was lacking in chances the second was drizzled with opportunity, as Alex Lawless netted for Town with just 47 minutes on the clock.
Scott Vernon and Jamey Osborne scored twice in quick succession to make it 4-1 and seemingly put the result beyond doubt with almost half an hour left to play.
Keen to salvage something Francois Zoko reduced the arrears on 75 minutes, but it served to be nothing but a consolation as the hosts closed the game out to earn all three points.
Darren Way was forced into one change from the side that impressively saw off Crewe Alexandra by a 3-0 scoreline on Easter Monday.
A late dropout in the lead up to the trip to Lincolnshire, Kevin Dawson missed the lengthy trip through injury allowing Ben Whitfield straight back into the side having missed three games through suspension.
Successful earlier in the week, the Glovers stuck with 4-4-2 as the Bournemouth loanee slotted into the right of a four-man midfield in a like-for-like swap with the Irish midfielder.
Bathed in Lincolnshire sunshine the Glovers started brightly with Otis Khan seeing plenty of the ball in the opening exchanges.
But before Town could put their early possession to use, they were dealt a blow when the Mariners won a penalty with their first venture forward.
The lively Jamey Osborne raced onto an angled through ball before being brought down by an advanced Jonny Maddison who had raced from his line.
Avoiding further punishment, Maddison took his spot on the goal line but couldn’t stop Jones converting from 12 yards.
The opener saw Russell Slade’s side settled into the game whilst Yeovil looked to regroup, as the half developed into one lacking in goal scoring opportunities.
With the ball spending most of its time in the middle of the park, neither ‘keeper found themselves truly troubled as the Mariners slowly cranked up the pressure.
Having enjoyed a spell of possession the home side doubled their lead with the game’s first meaningful attempt since the early opener, courtesy of Clements.
The midfield rode a challenge 20 yards from goal before picking out the bottom corner.
In an attempt to get back into the game before the break Jean-Louis Akpa Akpro notched Town’s first efforts on goal, glancing a header wide before seeing a rasping effort from range smash into the advertising hoardings.
As it was Way’s side headed in at half-time facing a two-goal deficit, needing to find a way to trouble home stopper James McKeown.
In a bid to do just that, Way switched to 3-4-3 at the break with Bevis Mugabi replacing Whitfield as Liam Shephard and Ryan Dickson pushed further forward.
The change in tactics had the desired impact as the Glovers got one back just 90 seconds after the restart.
Good hold-up play from Akpa Akpro saw him tee up Lawless just inside the box, with the Welshman emphatically driving home an effort for his first Yeovil goal.
The midfielder’s strike added to a bright start to the second half from Town, who were enjoying a sustained spell of pressure for the first time in the match.
But as the game reached the hour-mark the visitors endured a devastating spell which saw them concede twice in three minutes.
From a Danny Andrew corner, Vernon reeled off celebrating to leave Maddison appealing for a foul as he tried to punch clear, before Osborne got in on the act following a swift counter-attack to make it 4-1.
With seemingly little to lose the Glovers introduced Shayon Harrison and threw caution to the wind, a bold move which reaped some reward with 15 minutes left.
From a Matty Dolan corner, Zoko picked up the scraps to lash a shot into the roof of the net as the Somerset outfit looked to mount an unlikely comeback.
But that was as good as it got for Town who failed to beat McKeown once again, instead suffering a disappointing defeat to prolong the search for mathematical safety, despite the drop seeming unlikely with just two games remaining.
Grimsby Town: McKeown; Mills, Pearson, Collins, Andrew; Osborne (Bolarinwa 87’), Disley, Clements, Berrett (Vose 76’); Vernon (Dyson 71’), S. Jones.
Subs not used: Boyce, Davies, Comley, D. Jones.
Yeovil Town: Maddison; Shephard (Harrison 68’), Lacey, Smith, Dickson; Whitfield (Mugabi 45’), Lawless, Dolan, Khan; Zoko, Akpa Akpro.
Subs not used: James, Butcher, Goodship, Eaves, Sowunmi.