Fleetwood took an early lead through Steven Gillespie after Lee Fowler's bravery helped the home side break following a Wimbledon corner.
The striker, assisted by a slip from Yado Mambo, took his time before slotting a low shot past goalkeeper Seb Brown for his third goal of the season.
Wimbledon levelled just after the hour mark. Substitute Rashid Yusseff's free-kick from the edge of the area found Byron Harrison's head and the effort took a deflection past home keeper Scott Davies to hand the striker his fourth goal in as many games.
A late rally from Fleetwood saw them press for a win. David Ball and Barry Nicholson both had late chances for Micky Mellon's men. But, when Davies picked up a Youl Mawene backpass with just two minutes to play, the Dons were handed a golden opportunity to take all three points with a free-kick from six yards.
Fleetwood's wall on the line stood firm though, with George Francomb blasting the rebound over the crossbar.