George Francomb's first league goal for the Dons put the hosts ahead in the 50th minute but Banks struck shortly afterwards for the Spireites, who remain one point above second-placed Scunthorpe in the table.
Paul Cook's men, now without a win in three games, nearly went ahead in the first minute but Eoin Doyle's strike from 20 yards was well saved by Dons goalkeeper Ross Worner.
Wimbledon's first attempt came from a corner after some great work from Kevin Sainte-Luce, but Alan Bennett's header hit the crossbar.
Dons striker Danny Hylton then placed his free header, from six yards out, tamely into the arms of Chesterfield keeper Tommy Lee.
The deadlock was broken when former Norwich midfielder Francomb curled a fine shot from the edge of the area past Lee.
But five minutes later Chesterfield were level when Worner let Jimmy Ryan's cross slip from his grasp and Banks pounced to slot home.