And, boss Darren Ferguson will be hoping he can do a double by steering his side to the play-off finals in may. A feat Grimsby achieved over a decade ago.
Josh McQuoid poked the League One side ahead and Shaun Brisley's powerful header made it 2-0 at the break.
Eoin Doyle pulled one back from close range before Posh midfielder Joe Newell saw red for kicking out at Sam Morsy.
But Britt Assombalonga's penalty sealed victory after Mark Little was felled in the area by Liam Cooper.
Peterborough boss Darren Ferguson, watched by father Sir Alex, will hope victory boosts his side's faltering push for a place in the play-offs, withg his side currently occupying sixth spot and the final play-off place.
Posh boss Darren Ferguson has now won the trophy as a player and manager after scoring Wrexham's second goal in a 2-0 win over Southend United in 2005.
Chesterfiled, who won the competition under John Sheridan in 2012, will now be hoping to avoid the need to return to the national stadium in the play-offs. The Spireites are five points clear of fourth-placed Fleetwood with six games to play.