The first chance of the afternoon fell to Adam Rooney as he attempted to head the ball in from a corner for the visitors, but his glancing effort went just high.
Thomas Konrad forced a save down the end just a few moments later as he also looked to convert with a header from a corner, but his finish was straight into the hands of the keeper.
Dundee continued to create more chances, but it was Aberdeen who opened the scoring before half time when Rooney made a run into the box before unleashing a powerful strike into the bottom right.
Rooney tried to double the visitors' advantage just moments after the restart when a high ball forward left him with a chance with a header in the middle of the box, but his effort was punched clear.
The result leaves Aberdeen second in the table, while Dundee remain seventh.