Robert Page's late header ensured a winning start for new Blues boss John Sheridan in his first game in charge.
Paul Green opened the scoring with a sweetly-struck volley from the edge of the area in the 16th minute after Chesterfield failed to clear Lee Croft's free-kick.
However, the midfielder injured himself in giving the Championship club the lead and limped off to be replaced by Ben Pringle.
The Spireites restored parity early in the second half following a mazy run by Notts County target Jack Lester. His cut-back from the byline was slammed into the roof of the net from six yards by half-time substitute Scott Bowden.
Page capped a dominant second half display by the Spireites by heading home Gregor Robertson's short corner in the 83rd minute.