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Leicester looking dangerous every time they ventured forward threatened more goals but they reached half time with their noses just in front.
But the game turned early in the second half when Leicester full-back Frank Sinclair was sent off for dissent just minutes after being booked.
Three minutes later, on 54 minutes, John Oster headed in Alan Pouton's left-wing cross to put Grimsby level and sent in a real chance for all three points against high riding Leicester.
But Leicester made a couple of substitutions and gradually regained their composure.
They started to push forward and a spectacular scissor-kick from Turkish international Muzzy Izzet broke Grimsby's hearts with just over quarter of an hour to go.
Grimsby never gave up in front of their biggest crowd of the season but could not pull level a second time.
Leicester, beaten only for the third time midweek, had shown their intention from the start by playing with three men upfront.
But they had to readjust when Sinclair was sent off and showed their character to dig in and ride the storm.
Striker Paul Dickov might have added a late third, but that would have been rough justice on a Grimsby side once again fighting their customary relegation battle