Shaun Williams' first-half penalty and a fortuitous second goal from a Dean Bowditch free-kick saw the npower League One team overcome their Championship opponents at stadium:mk.
In a game of few chances, the hosts created the better opportunities as a much-changed Wednesday side struggled for cohesion.
Wednesday, with seven changes from the weekend, were forced to make another early change when Jermaine Johnson went off injured after just 12 minutes. Danny Mayor was his replacement. Either side of the substitution, Paul Corry tried his luck from long range but on both occasions Dons goalkeeper David Martin was not troubled.
The League One side went ahead in the 28th minute after referee Lee Collins spotted Lewis Buxton pulling at Bowditch's shirt inside the area. Williams confidently dispatched the resulting spot-kick past Stephen Bywater.
Mayor immediately threatened at the other end with a shot from the right-hand side of the area that went wide. Shortly afterwards Bywater had to push the ball away as Daniel Powell attempted to lob him from the edge of the box.
Ryan Lowe headed over the crossbar at the start of the second half and Bywater would have been grateful to see Gary MacKenzie nod the ball straight into his arms as the Dons continued to create the better opportunities.
Mayor went close again from the edge of the area on the hour mark before Martin made a routine save from Corry's 20-yard shot.
The second goal came with 15 minutes remaining. Bowditch swung in a free-kick from wide on the left and his intended cross eluded the runs of all his team-mates and the ball nestled in the bottom right-hand corner of the net.
The Dons came close to a third goal late on. After Martin Taylor had blocked shots from Lowe and then Williams, Bywater had to beat away another effort from the latter.