Jamie Winter opened the scoring for the visitors before Alan Goodall stretched the score before half time.
Adam Stansfield pulled one back for the Grecians after the break but Jack Lester struck a brace and some comical defending gifted further goals to Jamie Ward and Darren Currie.
Chesterfield had the first shot of the game in the first minute when Jack Lester forced Paul Jones to block his shot from the edge of the box.
Adam Stansfield went close for the Grecians when he volleyed narrowly past the post just midway through the half.
Steve Tully then fired over the bar after he was picked out by Bertie Cozic's fine pass as Exeter looked dangerous.
The visitors went ahead seven minutes before the break when Winter pounced on a loose ball and thumped an unstoppable shot past Jones from 25 yards.
On the stroke of half time Goodall broke into the City box and struck a deflected shot past Jones.
Exeter pulled a goal back four minutes after the break. Taylor and Marcus Stewart combined inside the box and when the ball broke to Stansfield he stroked it home from close range.
Chesterfield hit the third when Ward's shot was parried by Jones and Lester tapped home from close range.
The fourth came after a mix up at the back between Daniel Seabourne and Jones, leaving Lester to capitalise on the mistake and the knock the ball home.
Exeter's embarrassment was compounded when Tully was then robbed by Ward and the striker struck the fifth past Jones.
And in injury time Matt Gill was robbed in his own half and Currie completed the misery for the Grecians with a strike from six yards.