Dundee emerged with three points from a largely forgettable affair at Fir Park as Motherwell sank to the foot of the Scottish Premiership.
The only goal came from a mis-hit Paul McGinnn cross, which sailed over goalkeeper George Long into the net.
Well were a blunt force in attack throughout, creating barely a clear chance worthy of the name.
The Steelmen are now without a win in eight matches, while Dundee's top-six challenge remains in rude health.