Steven Gillespie fired Fleetwood into a seventh-minute lead but after Tendayi Darikwa had volleyed a 45th-minute equaliser, Atkinson settled it in cruel, last-gasp fashion.
The Cod Army went ahead when the hosts failed to get the ball clear following a corner and Gillespie found the bottom corner from 15 yards.
The visitors were the better side in the first half but just before the interval a long throw was headed out to Darikwa and his volley from the edge of the box took a slight deflection past Scott Davies.
Chesterfield improved in the second half and looked more likely to win it but when a free-kick was headed against a post, Atkinson could only turn the ball into his own net as he tried to clear.
