After a quiet opening quarter to the game the action suddenly heated up in the 25th minute when Darlington striker Richie Foran saw his goalbound effort, from a Franz Burgmeier cross, blocked five yards out.
From the resulting corner the Chesterfield goal again came under pressure when Jason Kennedy was left unmarked at the far post. The midfielder's shot was cleared off Tommy Lee's line thanks to some last-ditch defending from the Spireites.
A minute later it was the hosts who came under pressure at the back. Chesterfield winger Scott Boden crossed low from the left and the ball was hooked onto his own crossbar by Darlo captain Steve Foster.
In the 29th minute Burgmeier crossed from the right and a stooping header from Foran was easily claimed by Lee in the visitors' goal.
As the game moved towards the interval Chesterfield again threatened. A shot from the edge of the area by Jamie Winter was parried by Brown, the follow-up effort from Jamie Lowry was blocked inside the area by Neil Austin.
The second half began well for the Spireites as Lloyd Kerry fired inches over the crossbar in the 49th minute. Darlington responded with a lob from Kennedy that was pushed away by Lee in the 51st minute,
The hosts almost snatched the lead in the 64th minute when a corner from Rob Purdie was met by defender Alan White, who saw his volley fly inches wide with Lee beaten.
The Chesterfield keeper was again busy in the 73rd minute when diving to keep out a low drive from the edge of the area from substitute Billy Clarke.
Darlington brought on striker Pawel Abbott in the 74th minute for his first appearance of the season following a long injury lay-off, but the former Swansea man was unable to make an impact on the game.