The first match at Northampton had ended goalless, but the Cobblers put the replay to bed with two first-half goals and then sat back to comfortably hang on to their lead.
After a poor league performance at Scunthorpe on Saturday which saw them lose away for the first time this season, John Gorman's side gave a much improved display to brush aside their spirited opponents.
After two encouraging away displays at Northampton and Wycombe, Grimsby were brought back down to earth against a side who pipped them to promotion from League Two on the final day of last season.
After an even first period, Northampton went ahead on 17 minutes although there was some confusion as to the scorer.
A fine defence-splitting pass was contested by Justin Whittle and Scott McGleish but it was the Grimsby defender who was credited with the final touch.
Grimsby came back strongly and threatened a goal. Defender Nick Fenton and winger Nick Heggarty both went close but the best chance fell to striker Gary Jones two minutes before the break.
But he perhaps shot hurriedly and keeper Mark Bunn made a comfortable save.
This miss was a turning point as Northampton snatched the decisive goal with the last touch of the first half.
A suicidal ball played across their own penalty area by Grimsby was latched on to by Andy Holt and his cross was headed home by Joe Burnell for his first goal for the club.
That effectively was it, although Grimsby did start the second half brightly with top scorer Peter Bore having replaced Heggarty for the second period.
They needed a goal to make a match of it but so well-organised were the Cobblers that there was never any likelihood of that happening.
The visitors sat back and defended in depth, inviting Grimbsy to break them down and, although there was no lack of effort from Alan Buckley's men, it was a task that proved beyond them.