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Kris Boyd opened the scoring after nine minutes, breaking clear of the static Dee defence to knock the ball beyond the advancing Scott Bain.
It was all square before the half hour when Kevin Holt calmly finished, helped by keeper Freddie Woodman's bizarre decision to race from his line.
Dee's Henrik Ojamaa and Killie's Rory McKenzie went close to winning it.
This was the day's only Premiership match due to the Scottish Cup, meaning both sides knew a win would allow them to move further away from the drop zone.
There was plenty at stake and Killie started the brighter, earning their reward in nine minutes. A hopeful ball forward caught the Dee defence out and Boyd got the better of Kevin Gomis before knocking the ball beyond Bain.
Killie keeper Woodman then made a fine stop with his legs to deny Mark O'Hara but the visitors' glove man was badly at fault when Dee levelled.
Cammy Kerr launched a high ball into the box and Woodman raced from his line but got nowhere near it, allowing Holt to calmly fire the ball under him for 1-1.
Henrik Ojamaa went close to a second for the home side but Woodman was up to the task this time, touching the striker's fierce low shot around the post.
Ojamaa was the first to threaten after the break with a curling effort from distance that sailed narrowly over before Conor Sammon drew a decent stop from Bain at the other end.
Dundee's Tom Hateley showed great skill on the right before firing in a cross-shot that Woodman stopped well. And the keeper had to repeat the feat soon after to deny Kostadin Gadzhalov with a back-post header.
Both sides continued to press for the winner with the excellent Jordan Jones trying his luck for Killie before Rory McKenzie forced Bain into a fine acrobatic stop with a dig from distance.
Dee substitute Faissal El Bakhtaoui could have secured all three points at the death but after cutting in from the right his shot drifted wide of the far post.
Dundee manager Paul Hartley: "I think it was (a fair result). We didn't play as well today, I though we were sloppy in possession, kept giving it away, and our decision making was really poor.
"They started better than us but we came into the game more and had some opportunities. But we have to play a lot better.
"We had opportunities but we sort of snatched at a couple of things and need a little more calmness and composure in the final third and in the box.
"Now it's about points. We do want to play well but it's so tight down at the bottom of the table, we want to get into the top six. We feel we've missed opportunities - last week we were 2-0 up and it was another home game today but we didn't perform the way we should have."
Kilmarnock manager Lee Clark: "It was frustrating, very similar to the game last week. I thought we were the dominant team, they had a spell for 10 minutes before half time.
"We are disappointed that we haven't taken three points once again but our level of performance is really high at the moment. We're playing some really good football. Players are playing with a lot of confidence, they are young and what they need to do is try to change these draws into wins.
"We could probably have done with eight more point from our performances but it's about winning as well, it's not just about playing good football.
"Unfortunately it hasn't happened but it gives me a lot of belief and encouragement that we can kick on for the rest of the season. We want the players to keep on doing what they are doing. Can we be more ruthless in the final third, I think if there's a slight criticism we go in the right positions without picking out the right type of ball.
"They are really young, we've got some terrific experienced players in their helping them. That's us four unbeaten in the league now so it means we go into a really tough game next Sunday (against Aberdeen) with lots of confidence.
"It's a positive thing (being in the top six), it's good for the players but it's so tight and that can flip on its head by the time we play next. There's not much to call between the teams so you just have to be consistent in the level of performance and hope that the results follow."
Match ends, Dundee 1, Kilmarnock 1.
Second Half ends, Dundee 1, Kilmarnock 1.
Attempt missed. Marc Klok (Dundee) right footed shot from outside the box is too high.
Corner,  Dundee. Conceded by Iain Wilson.
Attempt saved. Faissal El Bakhtaoui (Dundee) right footed shot from outside the box is saved in the bottom right corner.
Corner,  Kilmarnock. Conceded by Scott Bain.
Attempt saved. Rory McKenzie (Kilmarnock) right footed shot from outside the box is saved in the top centre of the goal.
Substitution, Kilmarnock. Callum Roberts replaces Jordan Jones.
Substitution, Kilmarnock. Nathan Tyson replaces Kris Boyd.
Kevin Holt (Dundee) is shown the yellow card for a bad foul.
Foul by Kevin Holt (Dundee).
Jordan Jones (Kilmarnock) wins a free kick in the attacking half.
Substitution, Dundee. Faissal El Bakhtaoui replaces Henrik Ojamaa.
Corner,  Dundee. Conceded by Freddie Woodman.
Attempt saved. Paul McGowan (Dundee) right footed shot from outside the box is saved in the bottom right corner.
Corner,  Dundee. Conceded by Miles Addison.
Corner,  Dundee. Conceded by Kristoffer Ajer.
Paul McGowan (Dundee) wins a free kick in the defensive half.
Foul by Sean Longstaff (Kilmarnock).
Attempt missed. Marcus Haber (Dundee) right footed shot from the centre of the box is close, but misses to the left.
Kristoffer Ajer (Kilmarnock) wins a free kick in the defensive half.
Foul by Marcus Haber (Dundee).
Substitution, Dundee. Craig Wighton replaces Kevin Gomis because of an injury.
Corner,  Kilmarnock. Conceded by Kevin Gomis.
Corner,  Kilmarnock. Conceded by Kostadin Gadzhalov.
Corner,  Kilmarnock. Conceded by Marc Klok.
Conor Sammon (Kilmarnock) wins a free kick in the attacking half.
Foul by Kevin Gomis (Dundee).
Substitution, Dundee. Marc Klok replaces Tom Hateley.
Attempt missed. Mark O'Hara (Dundee) header from the centre of the box is too high.
Corner,  Dundee. Conceded by Greg Taylor.
Attempt saved. Kris Boyd (Kilmarnock) right footed shot from outside the box is saved in the top centre of the goal.
Corner,  Kilmarnock. Conceded by Scott Bain.
Attempt saved. Jordan Jones (Kilmarnock) right footed shot from outside the box is saved in the bottom right corner.
Foul by Kristoffer Ajer (Kilmarnock).
Tom Hateley (Dundee) wins a free kick in the attacking half.
Miles Addison (Kilmarnock) is shown the yellow card for a bad foul.
Foul by Miles Addison (Kilmarnock).
Mark O'Hara (Dundee) wins a free kick in the defensive half.
Greg Taylor (Kilmarnock) wins a free kick in the defensive half.
Kilmarnock moved into the top half of the Premiership courtesy of an entertaining draw at Dens Park.