The Owls striker was caught by Dean Lewington as he broke into the area, and while there were some protests as to whether it was in the box or not, Windass dusted himself off and smashed it past Jamie Cumming.
While Dons stuttered to finding their groove, losing Will Grigg and Nathan Holland to injuries, they came alive in the second half and should have been level when Dan Kemp forced an excellent save from David Stockdale, and substitute Matt Dennis was denied a penalty deep into stoppage time as they fell to a second defeat.
‘Introduce me to the friendly billionaire’ says Dons chairman Winkelman
Dons drawn away to Championship side Watford in Carabao Cup second round
Training ground plans for the Bowl to be resubmitted in a matter of weeks
No rush to get in another striker after Grigg’s injury
MK Dons 1-0 Sutton United - Dons Rated
Following their opening day defeat to Cambridge United, Liam Manning made four changes to his side to take on Sheffield Wednesday, handing first starts to Bradley Johnson, Daniel Oyegoke and Louie Barry, and a second debut to Ethan Robson after making the switch from Blackpool in the summer.
Roared on by more than 7,000 supporters in the away end, Wednesday started brightly and could have been ahead inside the first minute when the ball dropped to Barry Bannan but his swiped effort was blocked by skipper Dean Lewington.
And it set the tone for the next 15 minutes as Dons struggled to get to grips with the pace at which Wednesday were playing. Like a week prior at Cambridge, the front four were pretty ineffective for Manning's side as they toiled against the Wednesday defence.
When it did click though, they were able to cause problems - Daniel Oygoke, making his first senior start, fired just over, before Will Grigg then snuck onto the end of a loose backpass, but David Stockdale denied him.
Just as the home side were beginning to get on top though, a loose leg from Dean Lewington sent Josh Windass sprawling in the box, and after dusting himself off, fired Wednesday into the lead from the spot.
Dons were dealt another blow just before half-time when Grigg pulled up holding his hamstring, replaced then by Matt Dennis.
Though both sides were looking a match for each other, Fisayo Dele-Bashiru should have doubled Wednesday's deep into the six minutes of stoppage time when he shrugged off Oyegoke, but Jamie Cumming palmed his effort around the post.
But while the first half was disjointed from a home perspective, it was a far more familiar MK Dons performance in the second half.
They spent almost the whole period on the front foot, and though Dons were dealt another injury blow when Nathan Holland limped out early in the half, were desperately unlucky not to come away with at least a point.
Goalkeeper David Stockdale was the villain when he was at Wycombe last season during Dons' failed play-off campaign, and once again proved to be the immovable object. He first denied substitute Dan Kemp with a terrific one-handed stop before then denying Louie Barry as well.
Even Dean Lewington got in on the act as Dons pressed on, firing in a fierce strike from the edge of the box after a lively move sparked by Dennis saw the hosts come close again.
The former Norwich striker then felt he should have been awarded a penalty deep into stoppage time when he was shoved to the ground in the box, but with nothing given, it left Dons to back-to-back defeats.
Referee: Anthony Backhouse
Attendance: 13,241 (6,512)
MK Dons: Cumming, Lewington, O'Hora, Tucker, Oyegoke, Robson (Grant 80), B Johnson, Holland (Kemp 53), Smith, Barry (Burns 80), Grigg (Dennis 40)
Subs not used: Ravizzoli, Lawrence, Jules
Sheffield Wednesday: Stockdale, Palmer, Vaulks, Heneghan, Bannan (Byers 77), Windass (Bakinson 77), Paterson, Famewo (Hunt 29), Dele-Bashiru, M Johnson, Ihiekwe
Subs not used: Dawson, Iorfa, James, Cow
Booked: Ihiekwe, Bannan, Paterson, Dele-Bashiru