Hawley tapped in the only goal of the game four minutes before the break to move the Iron to within three points of safety as the Dons' play-off hopes were ended.
The Dons dominated possession in a low-key first half, but lacked a cutting edge, with Patrick Bamford scuffing two chances straight at goalkeeper Sam Slocombe.
Jon Otsemobor also headed over Shaun Williams' corner from close range and Luke Chadwick drilled a shot just wide from the edge of the box.
But Scunthorpe were dangerous on the break and Mark Duffy had a low drive pushed wide by Ian McLoughlin and Paul Reid headed against the crossbar before Hawley bundled in Jimmy Ryan's low cross to put the visitors ahead in the 41st minute.
The Dons piled forward after the break, but Slocombe produced a string of fine saves to earn the Iron victory, acrobatically denying Williams, Chadwick, Dean Bowditch and Mathias Doumbe.
Scunthorpe almost doubled their lead late on when Anthony Forde blasted against the post and Hawley was denied by the boot of McLoughlin.