Stephen Gleeson headed against the post from Adam Chicksen's cross before the frame of the goal came to the hosts' rescue again with seven minutes left as Luke Chadwick was denied.
The visitors were left frustrated by their Southern League opponents, for whom Zac Barrett was heroic in goal, and the two sides will now replay at stadium:mk.
The Dons came close after 19 minutes when Jay O'Shea's corner was met by Antony Kay's downward header but Barrett pushed it away.
But the Lilywhites nearly snatched the lead completely against the run of play when visiting goalkeeper David Martin was forced to turn Luke Allen's effort around his near post.
The Dons should have finally broken the deadlock when Gleeson was denied by the upright from close range and Chadwick's superb strike rattled the woodwork late on.
Barrett then ensured the tie would go to a replay as he brilliantly tipped over Ryan Lowe's header from Dean Lewington's cross in the 89th minute.
- Sports & Recreation
- Stephen Gleeson
- Luke Chadwick