Craig Dargo came off the bench to score the goal which secured Kilmarnock's place in the SPL for next season. Killie dominated the match, but looked set to be frustrated by a dogged defensive performance by the Dens Park side.
In a poor first half, Kilmarnock had almost all the possession and territorial advantage, but it was Dundee who came closest to scoring.
The best chance in the first half fell to Iain Anderson after Kilmarnock keeper Alan Combe had flapped at Steven Robb's deep corner. Anderson controlled the ball on his chest, but screwed his shot into the side netting from six yards.
The only shot which was on target in the woeful first period was a tame 20-yard effort from Gary Locke which was easily held by Derek Soutar.
Kilmarnock had been forced to replace Gordon Greer with Danny Invincibile midway through the half, and Dundee's Brent Sancho was unable to continue after th break and was replaced by Neil Barrett.
Killie showed more urgency from the restart, and midfielder Gary McDonald had two chances to put his side ahead inside the first five minutes of the second half. He pushed forward straight from the kick-off and was only denied by a great last-gasp tackle from Bobby Mann on the six-yard line. Four minutes later, Leven teed him up on the edge of the box, but this time he took too long to line the shot up, and was blocked.
Killie looked to have scored a deserved opener in the 55th minute when Danny Invincibile struck a powerful volley sweetly from eight yards, but Soutar somehow managed to react and touch the ball over the bar to record a fabulous save.
The home side were camped in the Dundee penalty box, but once again could not break down a stubborn defence where Mann was as strong as ever.
Kilmarnock had a good appeal for a penalty turned down when Steven Robb clearly block Invincibile's cross with a raised hand, but Steve Conroy's whistle remained silent.
With the match heading for a dispiritng draw, Jim Jefferies opted to change his front line with nine minutes left, bringing on Craig Dargo and Colin Nish, and the change did the trick three minutes later. Peter Leven crossed from the left, and although Dargo could not connect properly first time, he was able to recover and squeeze the ball past a crowd of bodies and in off the post.