There was little excitement at either end in a low-key first half with neither keeper seriously extended.
But the second half was a much more open affair and Shrewsbury created a number of chances with their easy-on-the-eye attacking play.
Young striker John Marsden, on his Football League debut, twice turned sharply in the box only for his well-struck shots to be kept out by the agile Martin.
The Dons keeper also dealt well with a stinging volley from the edge of the box from Paul Parry, but saved his best to last when he somehow threw himself in the way of a close-range Aaron Wildig effort after the midfielder was expertly picked out by Joe Jacobson's teasing cross.
Dons only offered any attacking threat in the final 20 minutes but might have pinched all three points.
Shrews stopper Chris Weale needed to be at his best to tip over a stinging shot from sub George Baldock while Izale McLeod, another sub, was denied by a timely block from Parry as the scoresheet somehow remained blank.