Dyer struck less than a minute after Jamie Lowry had cancelled out Keith Andrews' first goal since New Year's Day, which had given the visitors a 42nd minute lead.
It was one of the few openings the Dons actually had in a disjointed first half which was dominated by a strong swirling wind.
Chesterfield had won their previous three games but top scorer Jack Lester had few glimpses of goal against a defence in which Sean O'Hanlon was outstanding.
The visitors showed why they had been so successful on their travels, but the final ball let them down and the first 45 minutes looked to be heading for stalemate until Andrews marked his return from a two-match ban with his 12th goal of the season.
Alan Navarro played the ball in from the right and Chesterfield's defence switched off to leave the Dons skipper with a tap in at the back post.
Chesterfield had created few chances of their own with David Dowson missing their best opening in the eighth minute, but they drew level in the 69th minute with a spectacular strike from Lowry.
Lester knocked the ball back to the midfielder whose shot from 25 yards was deflected into the bottom right-hand corner.
But straight from the kick-off, Dyer restored his team's advantage when he played a clever one-two with substitute Aaron Wilbraham before placing a low shot from ten yards inside the right-hand post.
Dean Lewington almost scored a third ten minutes from time with a 30-yard shot that came back off a post, but Chesterfield could not find a way back for a second time.