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Goals from Dean Windass, Steve Kabba and Rob Kozluk did the damage and though Grimsby glimpsed a comeback when Stuart Campbell scored, the Blades eased to victory after Mariners midfielder Alan Pouton was dismissed for a second yellow card. Michael Brown's late goal was the icing on the cake.
Windass put United ahead in the 12th minute after Grimsby failed to clear their lines from a corner, sidefooting home from eight yards from a left-wing cross.
It was no surprise because they had already flashed the warning signals, Peter Ndlovu knocking a shot wide when goalkeeper Danny Coyne made a hash of a clearance, and Kabba heading over the top from a Brown free-kick.
Kabba - still Grimsby's leading scorer with six goals in an early-season loan spell - also went close when Coyne kept out his flick, but he finally got on the scoresheet in the 25th minute when his right-foot shot beat the Grimsby keeper.
The game was virtually over when United made it three seven minutes later, Kozluk blasting a low 30-yard shot into the corner of the net for his first ever goal.
Grimsby player-boss Paul Groves had drafted in strikers Steve Livingstone and Darren Mansaram, but there was precious little threat from the home side until Campbell scored after 34 minutes, drilling a 20-yard shot low into goal after United failed to clear a free-kick.
United were on the back foot for a while and John Oster missed two chances to cut the deficit further in the second half.
But Grimsby's hopes ended when Pouton saw red for two bookings in the space of six minutes, first for a foul on Brown and then for a 57th-minute lunge at Kozluk.
United took charge again as Grimsby's 10 men tired, and Brown wrapped it up after 86 minutes with a superb left-foot shot angled across Coyne from outside the penalty area.