Jimmy Ryan looked to have sealed the points with a goal early in the second half but Max Porter pounced eight minutes from time to equalise.
Newport had fallen out of the play-off picture but Shaun Jeffers was close to giving them the lead when he curled a shot just wide in the sixth minute but it needed a diving save from Ian McLoughlin to prevent Jay O'Shea's volley putting Chesterfield ahead in the 21st minute.
Jeffers forced a fine save from Tommy Lee a minute later and Ryan dragged shot wide in the 44th minute but the midfielder opened the scoring in the 49th when his cross from the right sailed over McLoughlin and inside the far post.
O'Shea should have scored a second in the when Eoin Doyle played him in but he fired wide from eight yards and an offside flag denied Daniel Kearns following a flowing Chesterfield move in the 61st minute.
Marc Richards had a chance to finish it when Ryan sent him clear but his lob failed to clear McLoughlin and Porter stunned Chesterfield in the 82nd minute with a precise finish from the edge of the box.