Inside the opening 10 minutes Danny Collins gave the Mariners the lead, before Francois Zoko notched his fifth goal of the season in some style to level it up on 21 minutes.
Having grown into the game before the break the Glovers were put under pressure after the restart, and Scott Vernon ensured all three points for the hosts with a header on 71 minutes.
Darren Way made one change to the side that drew with Morecambe at Huish Park on Tuesday.
Aiming for defensive solidity on their travels, Bevis Mugabi came in for Otis Khan in a swap that saw Tom James move further forward into midfield.
The alteration saw the Glovers switch to a diamond in midfield, with James at the base and Alefe Santos at the tip behind the strike pairing of Zoko and Sam Surridge, who were both on the score sheet in midweek.
As a steady drizzle fell in Lincolnshire the hosts were quick to get on the front foot through a flurry of set-pieces.
Artur Krysiak was routinely called into action to claim Collins’ header following a James Berrett wide free-kick, before the combination combined more potently on eight minutes.
From a Berrett corner, Krysiak couldn’t connect with his deep delivery allowing Collins to head home at the back post.
A disappointing start was almost made worse when Martin Woolford unleashed a venomous effort from range five minutes later, but Town’s stopper was equal to the effort with a smart diving save.
Having survived the initial storm the Green and Whites started to contain their opponents, before punishing the Mariners with a devastating counter-attack.
Picking up a loose ball, James Bailey instantly fed Surridge who’d arched a run in behind, which the Bournemouth loanee tried to shift onto his right foot.
Ricocheting off a home defender it kindly fell to Zoko who superbly curled a first-time effort past a hapless James McKeown from 20 yards to level the scores.
With Town’s diamond formation proving effective, Russell Slade’s side were only able to threaten Krysiak’s goal from set-pieces.
Just past the half-hour mark Nathan Clarke glanced a Woolford corner wide from close range, as he tried to join his defensive partner on the score sheet.
Krysiak was called into action once more in the first-half to push Woolford’s low shot from the angle round the post, before the Glovers ended the half in the ascendency.
McKeown wasn’t to be tested, but both James and Santos were notably starting to pull the strings as both sides headed into the break.
However, having had the chance to speak to his players during the interval, Slade’s side came out reinvigorated in the second half.
Exerting real pressure on the Glovers, the visitors were penned in as the game ticked past the hour mark, as the 3,900 home supporters grew in volume.
Unable to make it stick up front, Town continued to concede territory and were punished with a little under 20 minutes remaining.
Paul Dixon’s deep free-kick was headed back across goal by Clarke which substitute Vernon pounced on to leave Krysiak with no chance.
Grimsby’s second saw Way introduce Khan and former Mariner Rhys Browne, as Town emptied their bench of attacking options in a bid to get back into the match.
With the clock ticking Jake Gray squandered a chance to level things up, slicing an effort wide after Khan had burst along the byline.
That chance was soon followed up by Zoko heading into the arms of McKeown, as the Somerset outfit looked for a dramatic end to proceedings.
Despite a spell of pressure in the closing stages Town couldn’t trouble the Mariners further, forcing the wait for points on the road to continue.
Grimsby Town: McKeown, Davies, Clarke, Collins, Dixon, Dembele (Kelly 82’), Berrett, Summerfield, Woolford, Jones (Cardwell 90′), Matt (Vernon 66’).
Bookings: Jones 26’
Subs not used: Killip, K. Osborne, Hooper, Jaiyesimi.
Yeovil Town: Krysiak, Mugabi, Nelson, N. Smith, Dickson, Gray, James (Khan 73’), Bailey, Santos (Green 68’), Surridge (Browne 81’), Zoko.
Bookings: N. Smith 39’
Subs not used: Maddison, Alfei, Worthington, C. Smith.