Derby County: Prijovic brace launches Rams to win at Belper
Ben Pringle and Arnaud Mendy were also on target before the break and substitutes Greg Mills (2) and Henrik Ojamaa found the net late on.
Belper's goals came from Simon Barraclough and Aaron Pride, both fine strikes.
As in the match against Arnold Town a week ago, Derby fielded a team containing a mixture of first-team squad players and youngsters.
Martin Albrechtsen and Jordan Stewart started, as did Steve Davies and Giles Barnes.
Davies played 78 minutes on his return to action following an injury scare last week when he felt some discomfort in the foot he broke last season.
Pringle, who impressed against Arnold and Chesterfield, was in central midfield and will travel with the senior squad to Devon today for the Rams' three-match tour.
There was a nice touch before kick off when the Belper director and secretary, Dave Loughlin, received a memento to mark his 30 years service to the club.
Belper started brightly and went close three times in the opening 10 minutes.
Ross Atkins did well to tip the ball over after it appeared to come off a Derby defender, possibly Mark Dudley, and then the Rams goalkeeper saved with his legs when Dean Oliver was in on goal after a neat exchange of passes.
Richard Haigh's shot on the turn was gathered by Atkins but Derby went ahead on 11 minutes through Prijovic who, with time and space, coolly slotted the ball wide of Walker.
The Belper keeper had earlier done well to keep out a shot from Davies with his legs when going the wrong way, but he was beaten again on 20 minutes.
Having denied Pringle a minute earlier, Walker could do nothing when the midfielder found the corner of the net with a low drive after being set up by Stewart.
Belper's spirited first-half show was rewarded on 31 minutes when they pulled a goal back.
Lee Stevenson's deep corner reached Barraclough at the back post and the striker, falling backwards, did well to control his volley and beat Atkins.
But two goals in seven minutes shortly before the break put Derby firmly in control. A 25-yard strike from Mendy scorched high past Walker and into the keeper's top right-hand corner before Prijovic grabbed his second goal to make it 4-1.
The Serbian forward rose early to meet Davies' corner and although his glancing header was hacked clear, the ball had already crossed the line.
Alex Forde and Mills came on for Dudley and Pringle at half time but it was a Belper substitute who made an impact nine minutes into the second half. Pride moved forward from right-back and decided to try his luck from fully 30 yards. It proved a good decision as his shot flew beyond the dive of Atkins and in off a post.
Belper were inches away from a third goal on 65 minutes when their two strikers combined neatly.
Barraclough put Oliver in with a clever pass and he held off his marker to fire a shot across goal and just beyond the far post.
But Derby regained their three-goal cushion again 11 minutes from time.
Stewart put Mills in and the youngster calmly rolled his finish wide of Tom Pressman.
There was still time for Ojamaa to convert Forde's cross and then, with 90 minutes on the clock, Mills showed his pace to run clear and beat Pressman to make it 7-2.
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