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The division's bottom two clubs met at Tannadice on Tuesday, and Stephen McManus headed Motherwell into the lead in first-half injury time.
United began the second half on the front foot and hit the woodwork through Blair Spittal, but McDonald all-but sealed the points for the visitors when he nodded home Josh Law's corner 19 minutes from time.
And McDonald added gloss to the scoreline eight minutes later with an excellent long-range drive, as Motherwell claimed their first win in six Premiership outings.