Redditch United found Grimsby striker Alan Connell too hot to handle as they were well beaten 3-0 at Blundell Park.
The former Hereford front man netted in each half as the Mariners proved too strong for the inexperienced Reds.
Michael Coulson's 12th-minute strike put Grimsby on their way before Connell doubled the lead 12 minutes later.
Connell then took his tally for the season to 17 goals when he put the result beyond any doubt when he netted his second on the hour.
Redditch manager Matt Gardiner told BBC Hereford and Worcester:
"You go into every cup tie wanting to win it but we had four players cup-tied.
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"Then we had two injured, one more ill on the day and, with only two substitutes, our options were pretty limited.
"But I have to say in fairness to the players, they have worked their socks off, as we haven't played for a month and it has been difficult to train."
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