The German side fell to 1-0 loss to NextGen champions Internazionale last month and looked a little off the pace in the opening exchanges.
Rosenborg started brightly, and were rewarded for the endeavour on 25 minutes when Vajebah Sakor found the net with a cool finish as the visitors were pressed back.
The Norwegian side also hit the bar, but could not find a second goal.
Dortmund remain bottom of Group Five without a point in the competition while Rosenborg move up to second place, three points behind group leaders Inter with a game in hand.
