After a goalless first half, the game finally came alive after the interval when Armand Gnanduillet scored his first goal in English football before Jack Lester made the game safe in the 83rd minute.
Chesterfield had suffered an early setback when striker Marc Richards had to go off in the 20th minute with a hamstring injury and despite dominating possession, the home side created little in a shapeless first half until Sam Hird dragged a shot wide from the edge of the box.
Both sides made changes at half time and Chesterfield substitute Gnanduillet struck in the 59th minute when he sidefooted Danny Whitaker's ball in from the left past Neil Sullivan.
The veteran goalkeeper kept his side in the match with a superb save in the 76th minute when he flew to his right to tip away a 20-yard drive from Drew Talbot but he was beaten again seven minutes from time.
Wimbledon were caught pushing forward and Gnanduillet broke away to put Lester in on the right and the striker beat Sullivan with a low shot across the keeper.