The hosts had most of the play throughout the contest but Sam Jones’ seventh minute opener put the Mariners on the front foot.
That was how it remained at the break, but a cruel Callum Kennedy own goal then a first-time shot from substitute Scott Vernon sealed defeat for Orient.
O’s boss Danny Webb kept faith with the side which won 4-0 at Newport County last weekend, though there were changes on the bench which saw Nigel Atangana, Rowan Liburd and Michael Clark return.
The hosts found themselves 1-0 down though with just seven minutes on the clock when Danny Andrew lofted the ball into the back post and Sam Jones was there to head home past a helpless Charlie Grainger in the O’s goal.
Orient remained undeterred by the early setback and with 13 minutes gone a lovely ball in from Kennedy was only punched clear by Mariners goalkeeper James McKeown, and though the O;s recycled the ball they were unable to test the keeper again.
Michael Collins played a lovely throughball for Josh Koroma but unfortunately the forward was just offside as the O’s continued to dominate possession without turning it into goalscoring opportunities.
Orient remained on the front foot and a low ball in from Parkes was pushed clear by McKeown, before the O’s forced a corner which unfortunately came to nothing.
On the stroke of half time the visitors almost doubled their lead when Vose tried his luck from a free-kick but Grainger did enough at his near post to push the ball behind for a corner.
It was a positive start from the O’s in the second period as well when some good link-up play between Moncur and Koroma resulted in the latter putting a ball into the box for Dalby who got the slightest of touches on the ball but it went wide of the target.
Orient remained on the front foot and Hunt curled a free-kick just over the bar as the hosts continued to create the majority of the opportunities.
Jones fired acrobatically wide for the visitors, before Hunt produced an expert block to deny another goalscoring opportunity for the Mariners with an hour gone and then Vose tried his luck only for Grainger to hold in the O’s goal.
All the O’s possession was immaterial though as with a lot of luck, Grimsby doubled their lead. Grainger had initially done well to deny Sam Jones, but the ball struck Kennedy and trickled into the back of the net to double the visitors lead with 19 minutes remaining.
Good solo play from Koroma almost got Orient a lifeline with little over 10 minutes on the clock as he kept tight control of the ball before curling an effort from just outside the box over the bar.
Koroma continued to be positive and he saw an effort hit the side netting, but time was ticking away if the O’s were to give themselves a chance of getting anything from the game.
And any chance of that went with three minutes remaining when Craig Disley’s lob of a throughball was smashed home first time by substitute Scott Vernon.
Orient still kept going and the last chance of the game came their way as Kennedy struck the post after a mazy run, but that proved to be it for the O’s ahead of the visit to Accrington Stanley on Tuesday.
LEYTON ORIENT: Grainger, Judd, Hunt, Parkes, Kennedy, Moncur, Collins, Alzate, Koroma, Semedo, Dalby (Abrahams 70).
SUBSTITUTES: Sargeant, Atangana, Mezague, Liburd, Ochieng, Clark.
BOOKED: Collins (62), Koroma (90+3).
GRIMSBY TOWN: McKeown, Andrew, Pearson, Disley, Vose, Mills, Bolarinwa (Osborne 56), Collins, Comley, Dyson (Asante 65), Jones (Vernon 82).
SUBSTITUTES: Davies, Boyce, Yussuf, Maxwell.
BOOKED: Mills (56).
GOALS: Jones (7), Kennedy Own Goal (71), Vernon (87)
REFEREE: Lee Swabey
ATTENDANCE: 5,288 (1,086 Grimsby Town fans)