On a day where keeping things tight early on was imperative, conceding after 30 seconds was the worst possible start but that's what happened when a cross from Maya Williams was tapped in at the back post by Amy Cotton.
It was two in the fifth minute when Daisy Barritt found Hope Brassington, her shot was tipped on to the bar by Emma Varnam but the rebound fell to Lily Skeldon who rifled home.
Varnam rescued Belper three minutes later with a great save from Williams.
However the third goal arrived on ten minutes when Belper only half cleared a corner and when the ball fell to Skeldon she unleashed an unstoppable shot into the corner of the net.
Three became four a couple of minutes later when Cotton got in behind the Nailers defence to score her second.
The fifth goal arrived almost straight from the restart when Cotton's cross was turned in by Brassington.
Belle Peach should have made it six shortly after but her shot was over the bar.
On 20 minutes Derby got their sixth goal when Skeldon completed her hat trick with another fine strike when cutting in from the right.
A great long ball on the half hour found Cotton who rounded Varnam before slotting home number seven to complete her own hat trick.
Varnam produced another great save from Brassington who had been played in by Skeldon but the eighth goal arrived soon after.
In the 37th minute a cross from the right found Williams who scored at the back post.
Two minutes later Cotton found herself through on goal and despite a great challenge the rebound fell nicely for her to slot home number nine.
The Ewes went into double figures five minutes before half-time when after Belper struggled to clear Skeldon scored again.
Belper were much more resilient in the second half after bringing on some fresh legs and never stopped running, restricting the visitors to three goals.
The first came on 54 minutes when substitute Luci Cecchini ran on to a long through ball to make it eleven.
Five minutes later came number twelve when Brassington scored from the edge of the box.
Belper rarely threatened the Derby goal but on the hour mark the Ewes gave the ball away and Alice Faulding ran through but her attempted lob was just over the bar.
On 66 minutes Brassington was played in but her shot was wide.
In the 75th minute a mix-up in Derby's defence led to a chance for Faulding but Leilani Lovell produced a save from the one on one.
The final goal came with three minutes remaining when a cross from the right found Brassington who slid in to score and produce the third hat trick of the afternoon.
Luke Jackson and his team threw everything they could at their opponents but in the end Derby were too strong and progress to the semi-finals of the Derbyshire FA Women's Cup.
Belper Town: Varnam, Pickard (C), Jeffrey, Claxton, Longdon, Carnelley, Bennett, Watson, Thompson, White, Faulding.
Subs: Layton, Buxton, Needham, Powles.
Derby County U21s: Lovell, Sharp, Dickens, Peach, Cotton, Trail, Shepherd, Barritt, Skeldon, Brassington, Williams.
Subs: Strutt, Jasper, Cecchini, Qose.
Referee: Rhys Watkinson
Attendance: 70