Glossop started the game with midfielder Ben Richardson in goal, regular goalkeeper Luke Pilling was stuck in traffic on the way to game and missed kick-off, but was later substituted on just before half-time.
The home side went ahead from the penalty spot ten minutes into the second half, Phil Watt pulled down Glossop captain Kieran Lugsden as he drove into box and Jamie Rainford sent Charlie Mansfield the wrong way from the penalty spot.
The Nailers equalised with a penalty of their own, Tyrell Shannon-Lewis was fouled by Martin Parker after he had chased down a long ball, and Alex Steadman stepped up and slotted the ball home.
Steadman got his and the Nailers second five minutes later, he raced through one and one and Pilling could not get enough on the ball as Steadman side footed it past him.
The Hillmen were reduced to men in stoppage time when Eddie Moran was sent off for a second bookable offence, the linesman consulted the referee after he felt dissent was aimed his way and Moran was given his marching orders.
The win takes the Nailers through to the semi-finals of the Derbyshire Senior Cup and only one win away from a potential trip to the iPro Stadium.
Glossop North End: Richardson (Pilling (GK) 44'), Lugsden, Smart (Young 78'), Parker, Barnes, Andrews, Carey (Mulholland 78'), Rainford, Bailey, Lugsden (Capt.) Moran. Unused subs: White, Russell.
Belper Town: Mansfield (GK), Allen, Leggitt, Parker, Palmer, Watt, Stevenson, Graves (Capt.), Garnett (Shannon-Lewis 45'), Williams, Steadman (Constable 82'). Unused sub: Haystead
Referee: Nigel Smith (Chesterfield)
Attendance: 190