Adam Rooney secured a share of the spoils just as Dundee appeared to have earned the win with a Luka Tankulic goal shortly before half time.
The home side carved out the first opportunity when player of the year nominee Greg Stewart drifted in unchallenged from the left wing and curled a strike just wide of the Aberdeen goal from 20 yards.
But the Dons responded quickly and midfielder Peter Pawlett fired a vicious low drive which Kyle Letheren parried before the Dundee goalkeeper reacted to keep out the rebound from Cameron Smith.
And Smith then combined with Pawlett, who cut the ball back for Jonny Hayes but the winger’s shot was deflected behind for a corner.
Back at the other end of the pitch Dundee striker Tankulic sent a volley towards the corner of the net but Scott Brown got across to turn the ball around the post.
Lawrence Shankland was denied a goal four minutes before the break when his net-bound shot was blocked by team-mate David Goodwillie.
Instead, Dundee struck two minutes later when Donervan Daniels was short with a header back to Brown and Tankulic nipped in to lift the ball over the advancing keeper.
Five minutes after the interval James McPake put the ball behind under pressure from Goodwillie and from the resulting corner Ash Taylor flicked the ball over the bar at the near post.
Barry Robson then had a powerful strike turned wide by Letheren after a scramble inside the Dundee penalty area.
Dundee pushed for a second goal in the latter stages as Stewart jinked his way into the box before slicing an effort wide of the post before Paul McGowan chipped Brown from the edge of the box, but the ball dropped over the bar.
Rooney had the final say though when Aberdeen won a late corner and he scrambled the ball over the line from close-range.