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.
Full Time The final whistle goes and the game is over.
Effort from deep inside the area by Richard Brittain misses to the right of the goal.
Free kick awarded for a foul by Alex Cooper on Gary Irvine. A cross is delivered by Ryan Conroy, Declan Gallagher takes a shot. Mark Brown makes a save.
Colin Nish produces a left-footed shot from deep inside the six-yard box which goes wide of the left-hand upright.
Booking The referee books Gary Irvine for unsporting behaviour.
Substitution John Baird goes off and Mark Stewart comes on.
Corner taken by Richard Brittain, Gary Glen produces a left-footed shot from close range which goes wide of the left-hand upright.
Free kick awarded for a foul by Declan Gallagher on Colin McMenamin. Free kick taken by Iain Vigurs.
Matthew Lockwood crosses the ball, Grant Munro manages to make a clearance.
Inswinging corner taken by Richard Brittain from the left by-line, clearance by Colin Nish.
Iain Vigurs shoots direct from the free kick.
Booking Declan Gallagher is shown a yellow card.
Unfair challenge on Colin McMenamin by Declan Gallagher results in a free kick.
Ryan Conroy produces a cross.
Substitution Nicky Riley goes off and Ryan Conroy comes on.
The ball is swung over by Marc Fitzpatrick, Declan Gallagher makes a clearance.
Direct free kick taken by Rab Douglas.
Substitution Lewis Toshney replaces Kyle Benedictus.
Alex Cooper challenges Kevin McBride unfairly and gives away a free kick.
Richard Brittain takes a shot. Declan Gallagher gets a block in.
73:56 Goal scored
Goal! - Gary Glen - Ross Co 1 - 1 Dundee Gary Glen fires in a goal from the edge of the penalty area to the top right corner of the goal. Ross County 1-1 Dundee.
Kevin McBride takes a shot. Blocked by Scott Boyd.
The ball is swung over by Ross Tokely, Nicky Riley manages to make a clearance. Corner from the right by-line taken by Iain Vigurs, Declan Gallagher manages to make a clearance.
Ross Tokely produces a header from inside the area that goes over the crossbar.
Nicky Riley challenges Iain Vigurs unfairly and gives away a free kick. Strike on goal comes in from Richard Brittain from the free kick.
Header on goal by Colin Nish from inside the box goes harmlessly over the target.
John Baird sends in a cross, clearance made by Scott Boyd.
Unfair challenge on Colin McMenamin by Declan Gallagher results in a free kick. Richard Brittain takes the direct free kick.
Substitution Gary Glen is brought on as a substitute for Mark Fotheringham.
The ball is sent over by Richard Brittain.
Inswinging corner taken by James McAlister, Ross Tokely manages to make a clearance.
Foul by Colin Nish on Scott Boyd, free kick awarded. Free kick taken by Mark Brown.
Colin McMenamin is flagged offside by the assistant referee. Rab Douglas takes the indirect free kick.
Kevin McBride produces a right-footed shot from long range which goes wide right of the goal.
Matthew Lockwood takes the direct free kick.
Booking The referee shows Iain Vigurs a yellow card.
Free kick awarded for an unfair challenge on John Baird by Ross Tokely.
Kevin McBride takes the free kick.
Booking The referee cautions Mark Fotheringham for unsporting behaviour.
Mark Fotheringham challenges John Baird unfairly and gives away a free kick.
Alex Cooper sends in a cross.
Iain Vigurs takes a shot. Save by Rab Douglas.
Alex Cooper takes a shot. Save by Rab Douglas. Inswinging corner taken right-footed by Richard Brittain, save by Rab Douglas.
The second half has started.
45:00 +1:12 Half time
Half Time The referee calls an end to the first half.
Outswinging corner taken from the right by-line by Richard Brittain, Ross Tokely takes a shot. Save by Rab Douglas. Richard Brittain takes a inswinging corner to the near post, clearance by Nicky Riley.
Free kick awarded for a foul by Iain Davidson on Colin McMenamin. Direct free kick taken by Richard Brittain.
Effort from the edge of the box by Nicky Riley goes wide of the right-hand upright.
Kevin McBride produces a right-footed shot from a long way out which goes wide right of the goal.
36:47 Goal scored
Goal! - Iain Davidson - Ross Co 0 - 1 Dundee Iain Davidson grabs a goal. Ross County 0-1 Dundee.
Corner taken by Iain Vigurs from the right by-line played to the near post.
The ball is sent over by Marc Fitzpatrick, save by Rab Douglas.
The ball is swung over by Nicky Riley, John Baird takes a shot. Save by Mark Brown.
Nicky Riley fouled by Marc Fitzpatrick, the ref awards a free kick. Kyle Benedictus restarts play with the free kick.
A cross is delivered by Alex Cooper, save by Rab Douglas.
Foul by Alex Cooper on Nicky Riley, free kick awarded. Kyle Benedictus takes the direct free kick.
Corner taken by Richard Brittain, save by Rab Douglas.
Nicky Riley crosses the ball, Ross Tokely makes a clearance. Corner from the left by-line taken by Iain Davidson, Mark Brown fouled by Declan Gallagher, the ref awards a free kick. Free kick taken by Mark Brown.
Alex Cooper takes a shot. Gary Irvine gets a block in. Corner taken by Richard Brittain played to the near post, Gary Irvine manages to make a clearance.
The referee blows for offside against Colin Nish. Mark Brown restarts play with the free kick.
Centre by Colin McMenamin, Rab Douglas makes a comfortable save.
Long range effort from Mark Fotheringham misses to the left of the target.
Foul by Iain Davidson on Stuart Kettlewell, free kick awarded. Richard Brittain restarts play with the free kick.
The official flags Iain Vigurs offside. Rab Douglas takes the free kick.
Iain Davidson challenges Scott Boyd unfairly and gives away a free kick. Direct free kick taken by Mark Brown.
Unfair challenge on Colin Nish by Mark Fotheringham results in a free kick. Direct free kick taken by Kevin McBride.
Free kick awarded for a foul by Richard Brittain on Matthew Lockwood. Direct free kick taken by Matthew Lockwood.
Unfair challenge on Gary Irvine by Alex Cooper results in a free kick. Direct free kick taken by Kyle Benedictus.
Grant Munro fouled by Colin Nish, the ref awards a free kick. Free kick taken by Mark Brown.
Foul by Scott Boyd on John Baird, free kick awarded. Direct free kick taken by Declan Gallagher.
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