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.
Dons centre-half Gary MacKenzie made his first start since September against his former club after recovering from hip surgery. Full-back Jon Otsemobor also returned from a month-long absence with a groin injury.
The defensive duo came in for Adam Chicksen and Williams, with the latter moving into midfield alongside Darren Potter replacing Ryan Harley.
With Izale McLeod cup-tied Alan Smith was recalled, allowing former Wednesday striker Ryan Lowe to lead the attack.
Owls boss Dave Jones made seven changes. Defenders Lewis Buxton and Miguel Llera and midfielders Jermaine Johnson and Kieran Lee were the only players to survive from the team that started the victory at Hull on Saturday evening.
Wednesday were forced to make an early change when 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 Buxton pulling at Bowditch's shirt inside the area. Williams confidently dispatched the resulting spot-kick past Stephen Bywater.
Shortly afterwards Bywater had to push the ball away as Daniel Powell attempted to lob him from the edge of the box.
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.