There was more frustration for banned Killie boss Kenny Shiels as the visitors dominated the game but failed to grab a crucial winner.
Kilmarnock cannot have played as meekly all season and their manager – who still faces another three games in the stands after he was punished for comments made about fourth official Andrew Dallas – did not enjoy the experience one bit.
The Clydesdale Bank Premier League stalemate was a chance for his side to close in on the top six and yet they could not overcome a Dark Blues team fighting for their lives at the foot of the table.
For long spells it was a mundane contest but Dundee will feel they could have wrestled all three points and closed the gap on 11th-placed St Mirren to just nine points.
But the draw with Killie leaves the gap separating them from safety at 11 and means their run without a victory now extends to eight games.
And yet they had chances. Jim McAlister netted with a fine strike from outside the box early on but saw it chalked off after Colin Nish had wandered offside in the build-up.
John Baird went close as well when he sent a volley from an acute angle crashing onto the woodwork.
But Killie clung on for their fourth stalemate in their last six encounters.