Paul Cook's side had enjoyed a dream start to life in England's third tier following their promotion from League Two, beating Leyton Orient and Rochdale in their opening two encounters.
However, the Spireites were brought back down to earth this evening as Benik Afobe's second-half strike proved enough to down the hosts.
Chesterfield started the better of both sides but had to wait some 30 minutes before threatening to take the lead.
Romuald Boco found Jay O'Shea, whose curling effort was deflected narrowly wide for a corner on 29 minutes.
The Dons grew into the encounter and almost moved ahead 10 minutes before the break, as Afobe latched on to Dean Bowditch's lofted ball but his acrobatic effort glided just over the bar.
The former Arsenal youth soon struck gold, however, as Afobe fired the visitors ahead on 49 minutes, beating two defenders en route to finding the bottom corner.
Cook's troops should have levelled matters on 72 minutes, when Oliver Banks headed straight into the arms of goalkeeper Ian McLoughlin from six yards out.
It was as close as the hosts would come to levelling up, and Karl Robinson's side held out for the win.