Brighton's suspended boss Roberto de Zerbi had a bird's eye view from the stands as his Seagulls dominated the game, with Brighton constantly pouring forward against a team 76 positions below them in the English football pyramid.
The home side went ahead in the sixth minute when Deniz Undav pounced on a loose ball in the box to score after Moises Caicedo's shot from distance was saved. But Grimsby held on to go into the break down just one goal.
Six minutes after the break, however, Brighton doubled their lead through Ferguson when the lanky centre forward expertly controlled a high ball from Alexis Mac Allister before turning on the spot to fire home.
Ferguson had the ball in the net minutes later for a goal that was ruled out for offside but he managed to get his second when he was put through by Undav, finishing with aplomb when he had only the keeper to beat.
Brighton made it 4-0 when Adam Webster scooped the ball into the box where Solly March scored with a stooping header for his eighth goal of the season before Kaoru Mitoma wrapped up the win at the death with a shot that was deflected in.
In Sunday's early game, Sheffield United came from behind twice to edge Blackburn Rovers 3-2 and move into the semi-finals. Manchester City thrashed Burnley 6-0 on Saturday while Manchester United host Fulham on Sunday in the last quarter-final.
