Stockdale made several fine saves for the Owls to follow up his heroics for Wycombe against the Dons in last season’s Sky Bet League One play-off semi-finals.
It was his defiance that allowed the visitors to hold on to the lead given to them by Josh Windass’ penalty and earn their first win of the campaign, following last week’s breathless draw with Portsmouth.
Although Wednesday started the brighter, it was MK Dons who had the game’s first big chance as Will Grigg intercepted a poor back pass only to be denied by the first of Stockdale’s saves.
The Owls were then awarded a penalty when Ethan Robson was judged to have fouled Windass in the area, with the forward then dusting himself down to score from the spot.
Fisayo Dele-Bashiru had a great chance to double the visitors’ lead when he shrugged off Daniel Oyegoke before charging into the area, but Jamie Cumming stood strong to save in the Dons goal.
The hosts posed a bigger threat after the break with Stockdale having to be on his toes to keep out efforts from Matt Smith and Dean Lewington
He then produced his best save of the lot by getting down low to his right to keep out Dan Kemp’s shot, as MK Dons’ wait for a first goal of the season went on.
Not surprisingly, Wednesday boss Darren Moore was full of praise for his goalkeeper’s display at Stadium MK.
Moore said: “When you look at some of the shots they had, they looked straight at him but that’s because his positional sense was good.
“The most pleasing one for me was the one that went clean through and even though the boy was under a bit of pressure from Ben (Heneghan), he got his shot off and then Stocky’s pulled that off.
“I’m really pleased for him to get a clean sheet as well, it will do him wonders.
“He was saying in there that that’s a start and we’ve shown that we can do it, and he’s right.
“As I said, he’ll take a lot of confidence from that, as we will do.
“In the second half, we dropped back and we allowed them a bit of possession and territory, which invited the pressure on.
“But I’m pleased they saw the game out, got the clean sheet and got the three points.”
Moore is still looking to add to his squad with Swansea City youngster Kyle Joseph heavily linked with a loan move to Hillsborough in recent days.
Asked about any move for the Scotland youth international, Moore said: “I can’t shed any light on that. We’ve been linked with all sorts of players, it’s not just him, it’s been all sorts.”
Milton Keynes Dons: Cumming, Oyegoke, O’Hora, Tucker, Lewington, Johnson, Robson (Grant 79), Barry (Burns 79), Smith, Holland (Kemp 53), Grigg (Dennis 41). Unused substitutes: Lawrence, Ravizzoli, Jules.
Sheffield Wednesday: Stockdale, Ihiekwe, Heneghan, Famewo (Hunt 29), Palmer, Dele-Bashiru, Vaulks,B annan (Bakinson 77), Johnson, Windass (Byers 77), Paterson. Unused subs: Iorfa, Dawson, James, Sow.
Referee: A Backhouse (Cumbria).