The League One side, who had humbled Manchester City and West Ham in the Carling Cup in the last month, could not overcome the team that is bottom of the Conference South.
A first-half goal from Matthew Warner was enough to give Bastingstoke only the second League scalp in their history but there could no complaints about the scoreline.
Chesterfield did not do enough to merit pulling the game out of the fire and although keeper Stuart Searle made two vital saves in the second half, they did not create enough chances.
Basingstoke defended with spirit and belief on a blustery day from the start and the warning signs were there before Warner found the net.
James Taylor shot over from the edge of the box and Warner saw a curling left-foot shot taken over the bar by the strong wind minutes before he scored.
Chesterfield lost possession in midfield and David Stroud set off on a run up the left before releasing Rob Watkins, whose cross was turned in at the back post by Warner.
The 21-year-old personal trainer deserved his moment of glory although Chesterfield might have turned the game around if Colin Larkin had gone over in the last minute of the first half.
The striker was put through by Paul Hall and appeared to be clipped by Searle but stayed on his feet as the ball ran out of play.
The second half saw Chesterfield pile on the pressure but Basingstoke's back four stood firm, although the introduction of Caleb Folan threatened to ruin their day.
The speedy striker almost equalised in the 68th minute when Wayne Allison chested the ball down but his low shot cannoned off the legs of the keeper.
Searle did well to keep out a low shot from Mark Hughes in the 74th minute but that was Chesterfield's last real opening.
Taylor could have settled it in the 89th minute when he was put through but delayed his shot and was crowded-out.
But it made no difference as the visitors survived four minutes of stoppage time before celebrating a victory that will go down as one of the most memorable in the club's history.