The veteran striker ploughed home an unstoppable header from substitute Alan Connell's cross for his second goal of a pulsating game as Sean O'Driscoll's men came from behind to climb into fifth position in League One.
Earlier Chesterfield took the lead on 17 minutes when Wayne Allison ploughed a header past Neil Moss after Steve Blatherwick flicked on Shane Nicholson's corner.
The Cherries then missed a good chance through top scorer James Hayter, but two minutes after the break they were level.
Fletcher tapped into an empty after Spireites keeper Marton Fulop tipped his header onto the inside of the post.
Sixteen minutes later Brian Stock put the visitors ahead with a superb 25-yard free-kick before Blatherwick looked to have earned a point for the home side when he nodded home another Shane Nicholson on 76.
But Fletcher popped up 30 seconds into stoppage time to claim a priceless three points in Bournemouth's hunt for a play-off spot.