Motherwell deserved to win this game but the killer punch, which had knocked out Celtic in their last home match, deserted them on this occasion.
Although outplayed after taking an early lead, Dundee were happy enough with a draw since it keeps them above Motherwell in the table.
The opening minutes saw some thoughtful football but offered little threat from either side, except for a half chance which home striker Dirk Lehmann slammed into the side netting.
The Well gradually began to find some space down the left wing and an aggressive run by Steve Ferguson created a shooting opportunity, which captain Derek Adams wasted.
His miss became even more costly in the 13th minute, when Dundee took the lead. Barry Smith's cross would not normally have caused problems, but goalkeeper Stephen Woods missed the ball, allowing Steve Lovell to head in at the back post.
Woods soon redeemed himself by racing from his line to stop Lovell latching onto a long ball from midfield.
Lehmann looked to be Motherwell's best hope of an equaliser and the German did find the net, unfortunately the side netting, with a 25th minute header.
Motherwell continued their improvement after half time and Stephen Pearson 's unselfish cutback deserved a far better finish from Ferguson.
But Motherwell deservedly pulled level after 55 minutes when Ferguson's cross eluded Lehmann, only for Jamie McFadden to score with a looping header.
Confidence suddenly rocketed in the home camp and full back Martyn Corrigan almost produced the goal of the season with a terrific long-range effort.
In the 62nd minute Ferguson's low finish was blocked and McFadden sent the rebound wide.
Dundee were living dangerously yet they might have claimed all three points at the death when Woods had to make a brilliant save to deny Jonay Hernandez