Paul Dickov was the Foxes hero completing a hat-trick in the final minute afterputting his side in command by converting two first-half penalties.
Dickov went close with a header from Trevor Benjamin’s cross after ten minutes when denied by a point blank save from Kelvin Davis.
Wimbledon hit back and should have taken the lead after 15 minutes when Neil Shipperley blazed Wayne Gray's cross over the bar.
Then, after Dickov had shot just wide from 15 yards, the visitors again went close on the half-hour mark when Gareth Ainsworth's cross from the left found Shipperley and his goal bound header was blocked by a brave save from Ian Walker.
But it was City who broke through on 32 minutes courtesy of a successful penalty from Dickov after Frank Sinclair was adjudged to have been held back inside the area by Jermaine Darlington.
And on 40 minutes Leicester doubled their advantage with a second penalty after Rob Gier was ruled to have handled James Scowcroft's cross inside the area.
Dickov stepped up again and smashed his penalty to the left of the keeper.
If the Londoners felt aggrieved by the half-time score they could have no complaints about Leicester's third, scored by Benjamin two minutes after the re-start.
Benjamin started the move himself sweeping a cross field pass to Jordan Stewart on the left and his centre ricocheted off a Wimbledon defender to Benjamin who shot beyond the unprotected keeper from eight yards.
But Wimbledon refused to buckle, and Walker had to be at his best to save from both Gray and Ainsworth.
But it was Leicester who were to have the last word when in the final minute of normal time Stewart's shot was spilled by the keeper, and Dickov was first to react side footing the loose ball in to an unguarded net for his 19th goal of the season.