Both sides had chances in the early stages at Stadium MK, with last season's top scorer Daryl Murphy failing to test keeper David Martin before ex-Blues forward Dean Bowditch curled a shot just wide of the right post moments later.
Town perhaps should have scored another when Freddie Sears raced into space on the flank and with Martin well off his line, the winger was unable to find the target with his lob.
Later in the half, Murphy found himself in a similar position to Sears and as Martin rushed out to deny the Irishman, the forward also failed to steer his effort into the net.
Ipswich continued to press early in the second half as Murphy eased past Kyle McFadzean before curling a shot wide.
The Dons arguably had their best period late on as Dean Gerken was forced to make consecutive saves from Ben Reeves.
However, despite Gerken making a third late save from Rob Hall, Ipswich held on to move two points above Cardiff City.