Competing in their first ever game in the third tier, Matt Fryatt struck in each half for the Foxes, whose vibrant performance left Dons manager Roberto Di Matteo in no doubt of the hard work required from his team if they are to preserve their League One status.
City had the Dons pinned back from the start and there were chances early on with a Fryatt free-kick deflected over and Lloyd Dyer firing into the side-netting from a tight angle.
Leicester's impressive persistence was rewarded with a lead on 24 minutes.
Fryatt latched on to Joe Mattock's through ball and, as he bore down on goal, was upended by Dons defender Sean O'Hanlon.
The visitors could have few grumbles about the decision and Fryatt exacted maximum revenge by stroking home the penalty with the keeper diving the wrong way.
Despite their domination, City were confined to just one other clear chance before the break when Steve Howard fired over from 12 yards.
City almost doubled their advantage soon after the re-start when Willy Gueret spilled Dyer's free-kick at the feet of Fryatt, but the Dons managed to scramble the ball clear before the hitman could pull the trigger.
The visitors threatened in a rare breakout just after the restart when Dean Lewington's free-kick fell to Aaron Wilbraham, but Paul Henderson was alert to his angled drive from six yards out.
The Foxes wrapped up the game on 83 minutes when the lively Max-Alain Gradel stole the ball from the dithering Jude Stirling before surging into the box and feeding Fryatt to his left who guided home from ten yards.