The visitors had the edge in both halves but in the end were indebted to a clever tackle from full-back Eddie Nolan, who superbly slid the ball away from substitute Jabo Ibehre just as the Dons frontman looked to be clear on goal.
Ibehre had been brought at the break on by the Dons to add a physical presence to the home side's front line.
Prior to that they had been made to play second fiddle to an Iron team showing plenty of enterprise but unable to get into the penalty area with any conviction.
Scunthorpe's best chances came from the edge of the box within two first-half minutes.
First Bobby Grant was unlucky with a dipping effort that home goalkeeper David Martin tipped over, then midfielder Oliver Norwood was only just off target after Grant had laid the ball off neatly.