The former Celtic goalkeeper prevented his side going two behind a minute later with an excellent stop to keep out Arnason's powerful free-kick.
Dundee rallied and enjoyed a period of concerted pressure before the break, although a Nicky Riley effort which deflected wide and a Stephen O'Donnell shot which was too easy for Brown proved to be the closest they went to an equaliser.
The Dons should have doubled their lead on the stroke of half-time when Clark's tantalising cross found the unmarked Josh Magennis but the Northern Irishman headed over from six yards.
Aberdeen were forced to make a couple of early changes in the second half when Arnason limped off and was replaced by Mawene before Clark picked up a hamstring injury and Chalali was given his debut.
Richard Foster thought he had extended his side's lead after 64 minutes when he reacted quickest to turn the ball home after Douglas had pushed Pawlett's drive against the post, but the goal was ruled out for offside.
Dundee dominated the closing stages and threw everything at the Dons, but the Clydesdale Bank Premier League side survived the onslaught to book their place in the third round of the competition.cat perches veterinary monitors
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