The midfielder, sent off at Blundell Park last season for a foul on Gary Childs, scored twice in the first eight minutes to set the Canaries on their way and in a strange reversal of fortune, he was the victim of a 42nd-minute tackle which saw Childs sent off.
Norwich went ahead inside two minutes, Eadie profiting from a mistake by Ashley Fickling to slip the ball past Jason Pearcey. However, Fickling then made amends by scoring from close range after a corner from Craig Shakespeare.
Pearcey then gifted Norwich the lead two minutes later when he controlled a Kevin Jobling back-pass, but allowed Eadie to take the ball off him and slide it home.
Norwich added to Grimsby's misery by grabbing a third in the 29th minute. Neil Adams' cross hit the top of the bar before being returned by Robert Fleck and Andy Johnson's shot deflected in off John McDermott.
After Grimsby lost Childs for a second bookable offence, Norwich coasted in the second half, adding a fourth from the impressive Keith O'Neill in the 80th minute, and could have made it five when Johnson hit the bar.
Grimsby Town: Pearcey; McDermott, Jobling (Gallimore, 45), Fickling, Shakespeare, Widdrington (Trollope 81), Childs, Forrester (Woods, 82), Livingstone, Mendonca, Black.
Norwich City: Gunn; Newman (Wright, 90), Mills, Eadie (Rush, 54), Polston, Sutch, Adams, Fleck (Akinbiyi, 87), Milligan, Johnson, O'Neill.
Referee: S Mathieson (Stockport).
n First Division Tranmere Rovers have gone six matches without a win after being held 0-0 at home by Oxford United last night. The closest either side came to a goal was in the 14th minute when Oxford's Bobby Ford hit the bar twice.Reuse content