Nadir Ciftci scored twice in the first half at Tannadice, while Stuart Armstrong, Ryan Dow and Brian Graham added the other United goals before Lionel Ainsworth’s late consolation.
United took just eight minutes to open their account as Ciftci’s back-heel sent Armstrong clear and the striker took the return pass to shoot high into the net.
Ciftci completed his brace four minutes before the break when he got on the end of a Gary Mackay-Steven delivery to beat the exposed Gunnar Nielsen.
Armstrong secured the points just after the hour mark when he completed a superb solo run with a powerful finish.
Motherwell were static in defence again on 72 minutes as Dow had time and space to control a long ball on his chest inside the penalty area before despatching past Nielsen.
Substitute Graham completed the rout nine minutes from time by sliding the ball under the Motherwell keeper.
There was still time for Motherwell to grab a consolation with a deflected long-range strike on 88 minutes from Ainsworth.
United almost doubled their early advantage when Ciftci sent Paul Paton clear and the United midfielder lobbed the advancing Nielsen, but Motherwell defender Stephen McManus got back to clear the ball off the line.
The home side felt they should have been awarded a penalty when McManus tussled with Dow, but referee Steven McLean waved away the appeals.
Motherwell squandered a chance to get back into the match four minutes after the break, but Keith Lasley crashed his shot over the bar from inside the box.