A changed City side looked weak early on with poor passing providing the Dons with opportunities to break forward and Alex Tapp went close after only four minutes with a left-footed low drive that fell just wide of Neil Cutler's left post.
Midfielder Adam Nowland seemed to be Stoke's main problem and he rattled the woodwork in the 22nd minute when he was given room to run and shoot just outside the area.
However, ten minutes later, after John Halls had conceded a free-kick from the same range, Nowland rifled home the ball into Cutler's bottom left corner to give the visitors the lead.
The half-time break seemed to rouse the Potters' spirits but their attacks were halted by a steady Wimbledon defence.
Even the addition of three substitutions by Tony Pulis couldn't break their back line.
Though under pressure the away side still had their fair share of chances and through counter-attacks Wayne Gray went close and Nowland burst into the area on the right and shaved the far post.
Chirpy Wimbledon manager Stuart Murdoch said: "It's a consolation for the players after a poor season so far and it gives us a chance to pit our wits against a Premiership side.
"I keep feeling like I come into press conferences and have to say the same things but I think everyone knows the situation at this club.
"We are doing everything we can and just haven't had the results at Milton Keynes but hopefully this will give us something."