Gary Glen's equaliser gave Ross County a point and means Dundee lie five points adrift at the foot of the Scottish Premier League.
Iain Davidson's first goal of the season boosted Dundee's chances of getting three points at Victoria Park.
Near the end of a drab first half, the midfielder thundered a 30-yard swerving strike past County's Mark Brown.
But substitute Glen lashed past Rab Douglas after Iain Vigurs and Richard Brittain had shots blocked.
This bottom-of-the-table clash would have provided rich pickings for any winner but in the end the teams had to be content with a share of the spoils.
County captain Brittain hit the post with what was literally the last kick of the game, leaving the Dingwall side, who are tenth, six points better off than the visitors.
The 37 minutes until the opening goal was largely devoid of action and entertainment apart from a deflected shot from Alex Cooper, son of County assistant manager Neale who challenged Dundee keeper Douglas as the best player on the park.
Then, completely out of the blue, the match sparked into life when the ball broke to Davidson who had all the space in the world to crash home a stunning shot.
The strike tantalisingly took a late swerve beyond Brown into the top right corner.
Nicky Riley missed a chance to extend Dundee's lead when his shot drifted past the post and Ross Tokely saw a header tipped over the bar by Douglas just before half time.
In the second half the ever-present Douglas dealt with dangerous crosses from Cooper and Vigurs before Tokely saw an effort go narrowly by.
The equaliser came after a period of intense County pressure when the ball seemed to ricochet about the Dundee box for an eternity before Glen crashed it into the net.
Dundee might have gone back into the lead had Colin Nish done more justice to his service from Ryan Conway.
Then the game reached a cliffhanging climax when Brittain's effort cannoned off the right post just as referee Alan Muir blew for full time.