Sheffield United play Championship rivals Blackburn in the final match-up.
The Blades stunned Tottenham Hotspur – who are fourth in the Premier League – on Wednesday while Blackburn upset Leicester City in their fifth-round fixture.
Grimsby produced the result of the round by winning 2-1 at Premier League bottom club Southampton to reach the quarter-finals of the FA Cup for the first time since 1939.
The last-eight ties will be played from 17 to 19 March.