A stunning first-half free-kick by Dean Moxey put Exeter in front and they stood up to everything Chesterfield threw at them until Jack Lester equalised in the 68th minute.
The visitors could have regained the lead but Steve Basham's penalty was brilliantly saved and Lester cashed in with his second to win the game.
The result was badly needed by Richardson, who had come under-fire from a section of the Chesterfield fans during Saturday's home defeat to Morecambe.
It looked as if he would have to run the gauntlet again when Moxey drove an unstoppable shot from 20 yards, over the wall and into the top right-hand corner and Chesterfield could not find a reply despite constant pressure.
Lester was foiled by keeper Paul Jones and a great last-ditch tackle by Troy Archibald-Henville denied Martin Gritton before half-time and the frustration mounted in the second half.
Jones twice saved well from Lester and also kept out a swerving long-range shot from Jamie Winter but Chesterfield finally levelled when Lloyd Kerry pierced the visitors' defence and Lester ran clear to fire low past Jones.
But Exeter responded with a swift counter-attack down the right and Harley's header struck the arm of Aaron Downes with the referee deciding it was deliberate handball.
Downes was booked for protesting but Tommy Lee plunged to his right to keep out Basham's well-struck penalty and, within minutes, Chesterfield were in front.
This time it was Peter Till who released Lester and the striker cut in from the left before beating Jones with a low shot that found the bottom right-hand corner.
Lee still had to make two late saves but Chesterfield deserved the points and the crowd had another reason to celebrate when midfielder Derek Niven came on for his first appearance since recovering from testicular cancer.