League One outfit Scunthorpe enjoyed the best chances of a drab FA Cup first-round affair, but Nicky Ajose, on loan from Peterborough, was wasteful in front of goal as the Dons hung on.
Wimbledon's first real opening came in the 29th minute as Christian Jolley slipped the ball to fellow striker Rashid Yussuf in the box, but Sam Slocombe got down low to his left to make a comfortable save.
After the break Brown was forced into a great low save to his left from Ajose's venomous shot in the 57th minute.
At the other end, Max Porter turned and hit a snap shot in the area after the ball had gone loose, but his effort rolled past the right post.
Duffy worked a great chance for himself in the 75th minute, but his powerful shot was well saved by Brown as the Iron failed to make the breakthrough.
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