Darlington made life difficult for the home side and could have taken all three points but for the reactions of goalkeeper Tommy Lee.
The visitors were forced to make late changes and Chesterfield dominated the early play but Darlington's defence held on and the second half was much more evenly contested.
Even so, Chesterfield will feel they should have made more of their possession and it could have been an entirely different story if one or two early openings had been taken.
Danny Hall saw a downward header go agonisingly wide in the 14th minute and then Ian Miller threw himself in the path of a goalbound shot from Martin Gritton.
But it was Darlington that almost took a surprise lead in first-half stoppage time when a 25-yard shot by Franz Burgmeier was acrobatically pushed over the bar by Lee.
The Chesterfield goalkeeper was forced to make another excellent save in the 50th minute when he dived full-length to his left to push away a Pawel Abbott shot and the visitors were more of a threat as the second half progressed.
Chesterfield still had most of the possession but the closest they came to scoring was nine minutes from the end when substitute Ben Algar almost ruined all Darlington's good work.
His pin-point cross from the left found Scott Boden charging in at the back post but his firm header bounced back off an upright and was cleared.
Darlington almost had the last word when Jason Kennedy got in behind the home defence but his goalbound shot was superbly blocked by Jared Wilson.