O'Shea curled home an exquisite 68th-minute strike to cancel out Neal Bishop's long-range opener for County, but the Dons' 100% home record came to an end in Tuesday night's League One encounter at stadium:mk.
County bossed the first half and Jamal Campbell-Ryce had a shot well-saved by David Martin before Bishop put the visitors ahead after 25 minutes, smashing a swerving 25-yard drive into the bottom corner.
Martin then superbly pushed wide a curling free-kick from Alan Judge as the Dons struggled to contain a rampant County in the first period.
The home side improved after the break and substitute O'Shea equalised after 68 minutes, curling a neat finish past Bartosz Bialkowski from the edge of the box.
Shaun Williams also had a rasping 25-yard drive tipped over the crossbar by Bialkowski, but despite late pressure, the Dons were unable to force a winning goal.