Despite a vastly improved showing after the break Terry Butcher's side were unable to claw back the two goals they fatally conceded in the opening quarter.
The enthusiasm and flair of Motherwell's young striker James McFadden was evident throughout but even he was helpless as the home side's potential for relegation deepened.
Dundee shot a killer blow with barely one minute on the clock. Steven Milne broke free on the left and found his way to the goal line before cutely cutting the ball back to Mark Burchill at the near post.
The former Celtic player made no mistake as his diving header rifled into the bottom right-hand corner of the net from six yards out.
Steven Craig was unfortunate not to level matters for the home side in the 14th minute, his 20-yard effort crashing off the crossbar and over.
Caballero, midway inside the Motherwell half and with the deftest of touches, clipped the ball through the home defence to the onrunning Milne. He took a touch before slotting the ball past Francois Dubourdeau and in off the right-hand post.
Skilful play from McFadden almost brought Motherwell a goal in the 34th minute but Julian Speroni was on hand to collect the striker's shot.
In the 56th minute Craig saw his terrific attempt from the edge of the box tipped over for a corner before a fabulous McFadden effort was turned away by Speroni just two minutes later.
McFadden and Craig continued to threaten and eventually their persistence paid off. With 13 minutes remaining Craig played the ball in from the left and McFadden touched past Speroni to leave himself with the easiest of finishes from three yards out.