The Dons took the lead after 18 minutes when Peter Leven converted a penalty after rookie goalkeeper Arron Jameson had tripped Keanu Marsh-Brown. Jameson, who was in for the injured Nicky Weaver, can count himself fortunate to have escaped a red card.
Wednesday soon found themselves two down with Daniel Powell turned in from close range following great work down the left from Marsh-Brown.
However, the Dons' hopes of leaving Hillsborough with a win were dented when Gary MacKenzie was sent off for a second bookable offence.
Leven would later follow him in for an early bath for a professional foul as the Owls hit back to earn a point through goals by Neil Mellor and Clinton Morrison.
Mellor slotted home after 69 minutes after a great run by Giles Coke, then Morrison completed the comeback by reacting to a flick on from a corner.