Saido Berahino, Lee Gregory and Barry Bannan gave the Owls a 3-0 lead in the first half before Tottenham Hotspur loanee Troy Parrott pulled one back for MK Dons before the break.
Though Darren Moore’s side were defensively disciplined throughout the second period, Scott Twine’s injury-time free-kick set up a nervy finish after the fourth official indicated there would be 10 minutes added on.
But fortunately for Wednesday the hosts couldn’t capitalise and they move up two places to fifth.
Scroll down for our player ratings.
9. Fisayo Dele-Bashiru fiires - 7
Replacing Luongo was never going to be an easy task but the young midfielder did well on his first start since February. Made a few of those trademark surging runs, which are so great to watch. Photo: Steve Ellis
10. George Byers - 7
Created the opening for the first goal with a good run and lovely pass into Gregory. Gave away the foul for Twine's free-kick, which set up a nervy finish, but generally back to his usual neat and tidy self after a bit of an off day last weekend. Photo: Steve Ellis
11. Barry Bannan - 9
Quite simply a magician. Incredible first-half performance topped off with an unbelievable strike to make it 3-0. Also collected two assists in a near-perfect opening period. Should never have to buy a drink in S6 again. Photo: Steve Ellis
12. Saido Berahino - 7
Strengthened his case for more starts with a typical poacher's finish for his eighth goal of the season to get the Owls off to a flyer. Photo: Steve Ellis