The home team started brightly forcing a couple of corners in the opening minutes but failing to trouble the Aberdeen defence.
Dundee's early pressure did pay off when they took an eighth-minute lead courtesy of Mark Fotheringham whose 25 yard free kick was curled into the top corner giving David Priest no chance.
Chris Clark saw his low drive saved by Julian Speroni with a quarter of an hour gone.
A mistake by Fotheringham gifted the ball to David Zdrillic 20 yards out and his low drive went just past the post with 25 minutes played.
Aberdeen were getting closer to an equaliser and a minute later David Zdrilic was unlucky when his left foot shot rebounded off the inside of the post.
A fierce left foot strike by Kevin McNaughton came off the head of Brent Sancho and went inches past the post 10 minutes after the interval.
With 61 minutes played, Aberdeen drew level when Chris Clark's close range effort was blocked by Speroni but Clark gathered the ball again and sent a pass into Leigh Hinds who poked the ball home.
Nacho Novo had the ball in the net with 20 minutes to go but the far side assistant had his flag up in the air for off side.
Aberdeen were pushing forward and forced a couple of corners in the final minute but could not find a winner.
Nacho Novo almost grabbed one for the home team in time added on when he broke into the box but his cracking right foot shot was turned around the post by the diving David Preece to make sure the game ended all square.