Mattie Pollock's first-half header had the home side ahead but goals from Callum Wright, Sidnei Tavares and Admiral Muskwe sealed City's progression from Group H.
Four changes were made to the side that impressively defeated Brighton & Hove Albion 4-0 in Premier League 2 last month, as Kasey McAteer, Adam Leathers, Khanya Leshabela and Muskwe all came in.
The youthful Foxes lined up in a 4-2-3-1 formation with Leshabela supporting Muskwe up front and Callum Hulme and Sidnei Tavares providing cover for the back four.
Grimsby, meanwhile, made eight changes from the weekend and were looking to recover from Saturday's FA Cup 3-1 defeat by National League side Dagenham & Redbridge.
There was little goalmouth action in the opening stages, though James Morton came closest to troubling the scoreline, heading narrowly over after rising highest from the corner.
City then created their first opportunity by Muskwe meeting a low cross from Thanawat Suengchitthawon and heading narrowly wide of the near post.
Morton was then involved again, laying off the ball for Town skipper Danny Rose to strike wide from the edge of the area.
Grimsby almost made City pay for losing possession in their own half as Vontae Daley-Campbell was forced to slide in to deflect Montel Gibson's curling effort wide of the post.
And the hosts would break the deadlock from the resulting corner. Pollock powerfully headed home George Williams' corner on 21 minutes.
Gibson could have doubled their advantage soon after, slaloming his way into the box before seeing a low shot blocked. Gibson again found himself in front of goal after Rose picked him out, but this time found Jakub Stolarczyk standing tall to block the goal-bound strike.
The Foxes were searching for a route back into the contest and could have found it when Suengchitthawon raced through on goal. He opted to square the ball across to Muswke, rather than shoot himself, but overhit the pass, before Wright's shot from range was deflected wide.
Back at the other end, substitute Ira Jackson drilled wide from a tight angle on the stroke of half-time, failing to increase Grimsby's lead.
Early in the second-half there was a golden chance for Pollock - but the Grimsby man failed to get a good connection on his shot from inside the six-yard box and City survived.
Ali Reghba proved lively, coming on as a half-time substitute and after driving towards the box, forced Oliver Battersby to tip his fierce strike over the bar, in what was a sign of things to come.
Two goals in as many minutes turned the game in Leicester's favour. Firstly, Tavares beat the offside trap and played it across the box for Wright, who had the simplest of tasks to tap home from a yard out.
Tavares soon put City into the lead for the first time in the game via his superbly taken free-kick that curled in at the near post from all of 25 yards out.
Wright then had a header saved and Daley-Campbell's low strike was well palmed away by Oliver Battersby before Muskwe sliced the rebound wide, as the visitors continued to dominate.
The Foxes would eventually find a deserved, third goal when Wright linked up with Shane Flynn, who sent a looping cross into the box that Reghba headed towards goal before Muskwe got the final touch and bundled it home.
Grimsby threatened late on when Williams' free-kick was flicked on by Ludvig Öhman and Stolarcyzk had to push the ball away, but Leicester saw out the final minutes to safely secure all three points.
Captain Callum Wright started the comeback by netting City's equaliser.
The equaliser, courtesy of Callum Wright, sparked Leicester into life and gave them the confidence to continue attacking in the second half.
The former Blackburn Rovers man's simple finish set them up for the two goals that would follow, including a sweetly struck free-kick from Sidnei Tavares.
Forward Ali Reghba made the difference for Leicester in the second half.
Ali Reghba changed the game when he came on as a half-time substitute, harrowing the Grimsby defenders into making mistakes and creating opportunities for his team-mates in the final third.
His ability to hold the ball up and bring others into play was vital in helping City get back into the game, before he assisted the final goal.
Where does it leave us?
Admiral Muskwe celebrates scoring City's third goal on 77 minutes.
The Foxes now sit top of the group with six points from their three games, having beaten Hull City on matchday one, and await the result of the final fixture between Grimsby and the Tigers to see where they will finish.
Elsewhere in the group tonight, Hull City defeated Harrogate Town 2-0 to move onto three points, one behind Harrogate in second and three behind Leicester.
Leicester City Development Squad
The Foxes have a two week break before they return to league action later this month.
The Foxes return to Premier League 2 action on Monday 23 November, facing West Ham United Under-23s at King Power Stadium (7pm GMT kick-off).
City: Stolarczyk; McAteer (Godsmark-Ford 45), Daley-Campbell, Leathers, Flynn; Hulme (Reghba 45), Tavares; Suengchitthawon (Fitzhugh 84), Leshabela, Wright; Muskwe.
Subs not used: Bosworth, Ndukwu, Arlott-John, Pennant.
Goal: Wright 58, Tavares 60, Muskwe 77.
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