Hartlepool United loanee Colin Nish grabbed his first goal for Dundee, but was unable to prevent his side returning to the foot of the SPL table.
Nish headed home a first half cross for the SPL newcomers at Dens Park, but a second half brace by Michael Higdon gave table-topping Motherwell all 3 points.
Former Hibernian man Nish could have grabbed a second goal after the break but his angled effort landed the wrong side of the post.
The result saw Dundee slide back to the bottom of the table, with a trip to Glasgow to face Scottish football giants Celtic coming next weekend.
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