A fourth straight defeat for Spireites brought to an end the managerial reign of Dean Saunders.
Swindon had lost their last six away matches, but still came away from the Proact with a resounding 4-0 win.
Goals in the opening 14 minutes from ex-Spireite Nicky Ajose and Louis Thompson set the scene before Jon Obika added a third early in the second half.
Saunders axed by Chesterfield
Dean Saunders sacking: Saunders’ time at Chesterfield in pictures
Danny Wilson and Nigel Clough lead the way to replace Saunders
But the fatal wound came ten minutes from time when Ajose converted after Fabien Robert’s dart forward.
That goal led to the afternoon’s first and very loud ‘Saunders Out’ chants coupled with fans voting with their feet with a mass dash for the exits.
Visit www.derbyshiretimes.co.uk for all the latest news and reaction to the sacking and the race to replace Dean Saunders.