The Spireites went 3-0 up before the break and Kristian Dennis completed the scoring in the second half.
Caldwell’s men should have gone ahead in the seventh minute when Ricky German reached a backpass before Jan Budtz and rolled the ball to Delial Brewster, but with the keeper stranded he saw two shots blocked.
German then linked up with Scott Wiseman who found Brewster and this time he fired over.
Veteran stopper Budtz kept the game level on 15 minutes with a fine save to deny Sam Hird’s header.
Brewster was off target again soon after, Jerome Binnom-Williams curling in a sublime cross that the striker ran onto at the back post and turned wide.
With 20 minutes gone both sides appeared to dispense with the niceities, Brad Barry caught by a late tackle and Wiseman fouling Liam Hardy before the pair indulged in some handbags that sparked a shoving match involving several other.
When Town took the lead just before the half hour mark it was no surprise that Binnom-Williams was involved. The left wing-back, having already put in some excellent crosses, whipped another in that Brewster met with a downward header that beat Budtz.
The second goal followed four minutes later, Brewster felled in the box at the end of a fine run down the right, Jordan Sinnott coolly dispatching the spot-kick.
Buxton’s best chance of the half came from a Chesterfield error, Laurence Maguire heading back to his keeper without realising Hardy was between them, Joe Anyon saving the day.
And seconds after that Town took the game away, Ricky German running at the defence and slotting home via a deflection.
A very young Spireites side didn’t enjoy the best opening 20 minutes to the second half, struggling to be cohesive.
But frontman Gozie Ugwu provided the necessary spark, winning the ball, driving at Buxton and finding Dennis who curled home with aplomb.
Buxton: Budtz, M. Williams (Meade 46), A. Williams (Osgathorpe 75), Ravenhill (Hassler-Cregg 68), Maguire, Young, Taylor (Torn 65), Abbott, Hinsley (Smith 46), Hardy (Ward 46), T. Williams (Stevens 69).
Chesterfield: Anyon, Wiseman, Barry, Hird, Maguire, Evatt, Binnom-Williams, German, Brewster, Sinnott, Wakefield. Second half: Dorel, McGinn, Smith (Holmes 77), Mitchell, Ugwu, Dennis, Donohue, Dimaio, Brownell, Ofoegbu, Hand (Fowler 83).
Referee: Mr N. Smith. Assistants: Mr A. Pashley, Mr B. Broadley.
Goals: Brewster 27, Sinnott 31, German 35, Dennis 67