Lee Richardson's side needed a win at the Crown Ground on Saturday after dropping out of the top seven last weekend, but on a desperately disappointing day in Lancashire for the Spireites, their play-off ambitions fizzled out.
Stanley had the majority of the early chances with Grant going close on a couple of occasions before former Liverpool trainee Jimmy Ryan had an effort cleared off the line and fired just wide after a fantastic solo run.
The closest the Spireites came was in first-half stoppage time when Jamie Lowry's goal-bound effort was hacked clear by Andy Procter.
But the turning point of the game came five minutes after the interval when Peter Cavanagh's long cross-field pass found Grant and his first-time volley from 25 yards flashed passed keeper Tommy Lee into the top corner.
And any hopes of a Chesterfield recovery were scuppered 12 minutes from time when their skipper and the division's leading scorer Jack Lester was given a straight red card for dissent.