With coaches Mark Crossley and John Dungworth in charge, the Spireites named a starting line-up which featured new signings Armand Gnandulet and Richard Brindley. Jack Lester and Mark Randall were also given run-outs.
The visitors took an 11th minute lead when Shaun Tuton fired home following a goalmouth scramble.
Belper's Chris Adam and Jon Froggatt both headed off-target before Mark Randall scored a 23rd minute equaliser from the penalty spot after ex-Spireite Andy Rushbury was ruled to have handled in the area.
Chesterfield improved towards the end of the half with Lester putting an angled shot wide and Brindley having a low drive blocked.
Gnanduillet (39) produced a fine finish after running at the heart of the Belper defence to put the Spireites ahead.
Chesterfield established a two-goal lead three minutes after the re-start when Jacob Hazel found the net with a header from a Randall cross.
Simon Harrison's first-time shot from distance went just wide, with Josh Barrington stranded, after the keeper's clearance went straight to him.
Another ex-Spireite, Steve Warne, reduced the arrears with a 65th minute header from a corner which took a deflection.
After Randall tried an ambitious shot from his own half which went wide, Harrison had a chance to equalise from the spot in the 75th minute. Harrison stepped up after Randall was penalised for a foul in the area but Barrington made a fine save diving to his right to turn the ball wide.
Gnanduillet seized on a loose ball and fired in a shot which was palmed away by Aaron Chapman.
Jonathan Wafula completed the scoring in the 83rd minute, finding the net with a header from a Conor Townsend corner.
Chesterfield: Barrington, Brindley, Townsend, Randall, Broadhead, Whittaker, Wafula, Scully (Hewitt 76), Gnanduillet, Lester (Bowland 88), Hazel (Slack 88).