Niall Ennis broke the deadlock after just three minutes. A CJ Hamilton ball into the box was met by a Grimsby player, but the block landed perfectly into the feet of the Blackpool forward - who sharply produced the finish from close-range.
Two chances quickly came Jamie Walker’s way in the search of an equaliser for the home side, with both being pushed away by Bailey Peacock-Farrell.
The second in particular was an impressive save by the Northern Ireland international - getting a strong hand on a fierce half-volley.
Back down the other end, there were chances for the Seasiders to double their lead.
A great run from Karoy Anderson saw the ball laid into the path of Hayden Coulson - who saw a curling effort pushed over the bar by the acrobatic Christy Pym.
Just before the break, there were some heroics from Peacock-Farrell to make another impressive save from close-range to maintain the Blackpool lead.
Following the restart, Josh Bowler came close to doubling the visitors’ advantage, hitting the crossbar after cutting in from the right.
It continued to be Peacock-Farrell who kept Grimsby frustrated, with another impressive reaction save keeping out a power strike from Cameron McJannet.
The Seasiders’ attacked back just moments after, but Ennis wasn’t as sharp in the box as he was during the first half, dragging an attempt wide after cutting inside.
From the resulting goal kick, Bowler was quick on the press to steal the ball, before slotting calmly past Pym.
After being stopped by Peacock-Farrell once, McJannet found himself frustrated again, seeing a header saved a point blank range.
A goal from Harvey Rodgers came in the 92nd minute, but proved too late for the home side to add another to take the game to penalties, with Blackpool instead re-extending their lead down the other end through substitute Kylian Kouassi moments after.
Here’s how the Seasiders performed:
7. Jordan Brown - 7
Jordan Brown provided his usual protection in front of the defence, but the midfield as a whole needed to be better in possession at times. Photo: Gareth Evans
8. Karoy Anderson - 7
Karoy Anderson's best moment was a superb bit of skill to run forward and create a chance on the edge of the box for Hayden Coulson during the first half. Photo: Gareth Evans
9. Hayden Coulson - 7
Hayden Coulson tested Christy Pym with a good shot in the first half in his newly adopted midfield role. Photo: Gareth Evans
10. Ilmari Niskanen - N/A
It was a heartbreaking competitive debut for Ilmari Niskanen, with the wing-back being forced off in the first half due to a shoulder problem. Photo: Gareth Evans
11. CJ Hamilton - 7
CJ Hamilton was a threat at times with his pace up front, and was involved in the build-up to Ennis' goal, but a bit more composure was needed in a couple of situations. Photo: Gareth Evans
12. Niall Ennis - 7.5
Niall Ennis showcased the exact reason Blackpool signed him permanently last summer, being both alert and clinical in the box to break the deadlock after three minutes. Photo: Gareth Evans