The replacement of Wayne Allison for Tcham N'Toya-Zoa gave the visiting side a breath of fresh air up front as both teams looked lively early on.
The Spireites forced the first opportunity when Alex Bailey tried his luck with a 25-yard drive.
However, Mark Goodlad caught comfortably in what would be a busy afternoon for the goalkeeper.
Vale almost opened the scoring themselves soon after but Billy Paynter could only stab wide his shot from a low Lee Matthews cross.
Jamie McMaster looked lively throughout and had his first real look at goal after 21 minutes.
His 20-yard effort forced another top-class save from Goodlad to deny the Australian striker.
Matthews found himself more involved in the game later in the half but poor finishing denied him a shot on target.
The Valiants broke the deadlock after 49 minutes when a superb Michael Cummins cross was met by the in-form Matthews.
The forward steered his header perfectly into Marton Fulop's bottom right corner from 12 yards.
Vale could have doubled their lead almost straight away but a lunging tackle deflected Michael Walsh's 15-yard shot over the bar.
Chesterfield were briefly left with 10 men late in the second half when Shane Nicholson had to rush to the changing room due to a bloody nose but Vale failed to take advantage.
The addition of Caleb Folan in the 83rd minute attempted to liven up the away side's attack but, just like the earlier substitute appearance of Allison, it had no effect.