Mark Wright gave the Dons an early lead but it was all Chesterfield after that as they outclassed the home side with goals in each half from Felix Bastians and Jamie Ward.
The Dons might have scraped a draw late on, but a Keith Andrews injury-time goal was disallowed.
It's only the Dons' third defeat they've incurred at home this season, and one they deserved.
The game started at a ferocious pace with the home side the brighter of the two teams. A good move down the left gave Chesterfield an early scare when Lloyd Dyer's dangerous cross was sliced clear by Gregor Robertson on just two minutes.
But the Spireites hit back soon after when Jack Lester should have scored after he controlled Felix Bastians cross and shot just wide of the post from 10 yards.
Chersterfield were made to pay as the Dons immediately went up the other end and scored. Another great cross from the left hand side by Dyer picked out Mark Wright who was left completely unmarked 10 yards out. Wright controlled then smashed the ball home for his seventh goal in 10 games for the club.
The visitors responded well and put the Dons under increasing pressure without creating many chances.
They finally got their reward after a long period of possession when Felix Bastians smashed home on 33 minutes. Drissa Diallo misjudged Adam Rooney's cross and the winger composed himself well to finish.
They continued to batter the Dons defence but skipper Keith Andrews almost gave the Dons an undeserved lead at half time when his 25-yeard effort landed on the roof of the net on 42 minutes.
Then on the stroke of half time Alan Navarro had a 20-yard effort well beat out by keeper Barry Roche.
Chesterfield started the second half confidently and were rewarded again on 52 minutes. Jamie Lowry picked out Ward superbly and the little striker slotted comfortably past Willy Gueret from ten yards.
On 58 minutes Ward could have sealed the points when he went through on goal again, this time Lester picked him out well, but he just shot past the post.
But the Dons almost got back in the game minutes later when Dean Lewington's dangerous free-kick was almost turned into goal by a Chesterfield player.
There was a dull period after that when neither side created much.
It looked like it just wasn't Dons' day, and that was confirmed when Andrews blasted a 30-yard free-kick high into the stands on 78 minutes.
On 81 minutes the impressive Ward had another chance to seal the game, pouncing on Swailes' poor clearance. The striker twisted his way into the box before Gueret smothered well at his feet.
The Dons laid siege to the Spireites goal in the closing stages and they thought they'd equalised when the ball rebounded of Andrews into the goal, but amid a flurry of confusion the goal was disallowed, the referee ruling he used his arm.