Second-half goals from Stephen Duke-McKenna and Armani Little sealed a deserved victory for the hosts.
Duke-McKenna struck the opener from the edge of the box after 70 minutes and then Little scored from the penalty spot after a foul by Jim Kellermann.
The Spireites were not at the races at all and put in probably their worst performance of the season.
After the game, the DT was informed that there would be no post-match reaction from the Chesterfield camp.
This is the second time that there has been complete silence after a match this season since Cook was appointed, with the other time coming after a 3-2 home defeat to Solihull Moors.
The loss leaves Chesterfield’s hopes of finishing in the play-offs hanging in the balance. They desperately need Dagenham and Redbridge, who are three points behind, to lose at Solihull Moors later this afternoon.
Defeat for Dagenham would mean Town, who host Woking at home next Sunday in the final match of the regular season, would have their destiny in their own hands.