Simon Johnson and Jamie McMaster scored United's goals and the young strike duo caused all sorts of problems for the Spireites' defence.
Johnson continues to look an exciting prospect and after spending a month of last season on loan at Coventry, McMaster is starting to look increasingly like the finished product.
His goal was a stunner, following a neat one-two on the edge of the box with Johnson he bent his shot into the top right hand corner of the net from the edge of the area, plus his all-round play suggested a new maturity from a player given just four substitute appearances last season.
Another bonus to come out of Saturday's win was the performance of forgotten Irishman Stephen McPhail. The midfielder was a second-half substitute at the KC Stadium, but he returned to action 24 hours later to dictate play with a range of incisive passes.
Frazer Richardson skippered the side well at the heart of defence, despite struggling at times against the stronger presence of the Chesterfield forwards, and 16-year-old Aaron Lennon underlined his huge potential after the break.
Lennon, a regular in the England under-17 set-up, was a half-time substitute for trialist Andy Watson. Lennon’s jinxing run saw him beat at least two men before he set Simon Johnson off on another goalscoring opportunity, except this time Johnson's curling shot hit the foot of the post and rebounded to safety.