Late goals from Luke Hinsley and Marcus Marshall turned the game on its head after George Milner had given Belper the lead.
After a slow start to the game, the first chance fell to Grant Black’s side. Craig Nelthorpe skilfully beat his marker before firing over.
Matlock’s first chance of the game came the way of captain Cleveland Taylor whose 25-yard drive just missed the top corner.
Belper’s best attacking threat, Piteu Crouz, advanced down the left before rolling the ball back to Cameron Clark who found the head of Nathan Curtis, but his header fell wide of the post.
The Gladiators almost took the lead a minute before the break. Jamie Jackson ran at his marker before finding veteran Craig Westcarr who twisted and turned but his low shot was blocked on the line superbly by Alex Peterson.
Half-Time: Matlock Town 0 - 0 Belper Town
The home side had two chances to break the deadlock shortly after half time. First, Westcarr beat the offside trap but Leigh Overton denied him before the keeper got up quickly to thwart the threat of Marshall.
The Nailers took the lead midway through the second half when Crouz again beat the full-back before firing across the face of goal for Milner to tap into an empty net.
Matlock drew level soon after when a deep cross found the head of Dwayne Wiley who knocked it back to sub Hinsley to emphatically volley the ball into the top corner.
Just a few minutes later, Belper had a chance to regain the lead. Milner played the ball through to Nelthorpe, but his effort was blocked behind by Lee Beevers.
The away side had a huge chance to take the lead. Nelthorpe went through on goal but decide against playing it to Milner and instead wasted the opportunity.
Belper had another chance going into the final ten minutes. Crouz was at the centre of it again as he fed the ball to Milner, but Jordan Pierrepoint made a superb save to keep the tie level.
Dave Frecklington’s side took the lead, against the run of play, with three minutes left. Taylor advanced forward and played a ball through to Marshall who kept his composure to guide the ball past Overton.
The Gladiators had the chance to secure their place in the semi-finals, but Hinsley was denied his second of the game after a fine save by Overton.
Matlock Town now go onto face either Alfreton Town or Buxton in the semi-final the week commencing 5th January.
Full-Time: Matlock Town 2 - 1 Belper Town
Matlock Town: 1. Pierrepoint; 2. Hare (16. Hollingsworth 56’), 3. Davie, 4. Taylor ©, 5. Beatson, 6. Wiley, 7. Jackson (17. Chapell 74’), 8. Beevers, 9. Westcarr (15. Hinsley 58’), 10. Marshall, 11. King.
Subs: 12. Wood, 14. Hall, 15. Hinsley, 16. Hollingsworth, 17. Chapell.
Belper Town: 1. Overton; 2. Hough (12. Assenso 74’), 3. Clark, 4. Robson, 5. South, 6. Peterson, 7. Crouz, 8. Gordon, 9. Milner, 10. Curtis (15. Hancock 83’), 11. Nelthorpe.
Subs: 12. Assenso, 14. Sturgess, 15. Hancock, 16. Esmaeily, 17. Thompson.