Lee Bonis, Chey Dunkley and Dilan Markanday all missed big chances for the Spireites before Liam Mandeville’s deflected strike put them ahead on 39 minutes.
Bonis squandered another good opportunity after the break, while Ronan Darcy struck the posts for the hosts, before Armando Dobra was denied by goalkeeper Jacob Chapman in the closing stages.
The Blues were on track for successive wins and clean sheets and those missed chances came back to bite them when Jay Williams headed in with the last touch of the game in the 95th minute.
The result means Chesterfield drop a place to seventh despite being unbeaten in six.
Here are our player ratings from the game...
1. Zach Hemming 6
Called into action early doors, saving from Orsi. His saves from Richards and Williams in the second-half were more routine. On course for another clean sheet but Williams' header - which was straight down the middle - somehow went past him. Photo: Tina Jenner
2. Sam Curtis 7
Made a great last-ditch block to deny former Spireite Darcy just after Chesterfield went in front. Always looked in control. Looks right at home. Photo: Brian Eyre
3. Chey Dunkley 7
Made a vital interception to halt a dangerous Crawley attack. Should have done better with a close-range header at 0-0 down the other end. Defended the box strongly, getting his head and a boot on things. Photo: Brian Eyre
4. Sil Swinkels 6
The Aston Villa loanee didn't have bundles of individual defending to do but he was dealing with what came his way - as well as keeping the ball ticking over in possession - but it did look like Williams got the better of him for the equaliser. Photo: Tina Jenner