Jacob Hazel scored from the penalty spot to give a youthful Spireites side an early lead but two goals from Massiah McDonald took Matlock to the final of the competition.
Hazel put away an 11th minute penalty after being fouled in the area by Martin Foster.
Anthony Griffiths-Junior and McDonald both put efforts off-target before McDonald struck a 37th minute equaliser after receiving a good ball from Foster.
Hazel made an appeal for a second penalty, which was waved away, after being challenged in the area by Adam Yates.
Matlock's James Ashmore saw his free-kick blocked by the defensive wall and also had a 20-yard effort saved before McDonald (67) met Lee Featherstone's cross with a header for the winner.
Hazel looked to have scored a second goal, only to see his goalbound shot hacked away with keeper Jon Kennedy stranded.
Josh Barrington comfortably saved Griffiths-Junior's low shot in the closing stages and McDonald put a low shot wide.
Matlock: Kennedy, Harcourt, Featherstone, Foster, Yates, Lukic, Grayson (Dennis 82), Ashmore, McDonald, Davies, Griffiths-Junior. Unused subs: Hindley, Laight, Travis, Buxton.
Chesterfield: Barrington, Slack (McNicholas 88), Clarke, Scully, Broadhead, Whittaker, Wafula, Hewitt, Bowland (Noel 70), Hazel, Fereday. Unused subs: Mason, Mathers, Brock.