Dundee came from behind to secure all three points with a goal in injury time by Fabien Caballero.
With just three minutes played a free-kick by Jonay Hernandez was easily saved by Gordon Marshall.
Gary Locke got forward, but shot well wide with a quarter of an hour played and a minute later Gavin Rae fired straight at Marshall from inside the box.
Midway through the first half David MacKay hit a poor shot straight at Marshall after his run saw him go past two Kilmarnock defenders.
With half an hour played a cross from the right by Garry Brady was met on the volley by nacho Novo but his shot was easily saved by Marshall.
Kilmarnock had the ball in the back of the net three minutes before half time but Alan Mahood's effort was ruled out for offside.
Lee Wilkie had his header from a Georgi Nemsadze corner cleared off the line in the first minute of the second half.
A minute later Julian Speroni saved a close-range effort from Samuel Boutal.
With 32 minutes on the clock Caballero saw his 30-yard effort blocked by Marshall.
With 65 minutes played Kilmarnock took the lead when debutant Boutal scored from close range from a Steve Fulton cross.
Ten minutes later Dundee drew level when Rae fired low past Marshall from the edge of the area.
Eight minutes from time Novo looked to have given Dundee the lead from ten yards, but Marshall got the slightest of touches and Novo's shot went inches past the post.
With a minute of injury time played Dundee grabbed the winner when Caballero played a one-two with Novo to fire past Marshall from eight yards