Goals from Trevor Benjamin and Callum Davidson - his first of the season - edged Leicester closer to the Premiership, but pushed Grimsby closer to relegation.
City were without regular strikers Paul Dickov and Brian Deane so James Scowcroft was switched from midfield to partner Benjamin in attack.
And Benjamin almost gave City a first-minute lead when his spectacular overhead kick flew just over.
Grimsby, hit by injuries and suspensions, struck back on six minutes when they almost took a shock lead when a John McDermott cross fell to Darren Mansaram who seemed certain to score until Gerry Taggart got a foot in to divert the strikers shot out for a corner.
And after both Benjamin and Scowcroft had failed to connect with a cross from Jordan Stewart Grimsby threatened again with Paul Groves heading just over.
But City slowly tightened the screw and amid mounting pressure Matt Elliott went close when he prodded a Muzzy Izzet corner just wide and Trevor Benjamin almost found the net with a 20-yard drive.
A minute before the break Danny Coyne came to Grimsby's rescue when he kept out Jordan Stewart's 25 yard shot with a stunning fingertip save.
Soon after the restart Izzet fired a 22-yard free-kick straight at Coyne and soon after the keeper again denied Leicester, this time diving full stretch to keep out Benjamin's 20-yard drive.
After Chris Bolder had lifted a 12-yard shot over the bar the Foxes finally broke through on the hour mark.
Alan Rogers got away on the left before finding Scowcroft at the far post and he knocked the ball across the face of goal for Benjamin to score with a diving header.
And City gave themselves a two-goal cushion on 70 minutes.
Coyne again did well to beat out Stewart's shot from 12 yards but the keeper could do nothing to prevent Davidson from side footing the loose ball into an unguarded net.
Grimsby might have made life difficult for Leicester had Steve Livingstone not had a goal ruled offside with six minutes left.
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