Di Maria opened the scoring midway through the first half as his left-footed free-kick evaded everyone and beat Rob Green to his right.
Ander Herrera doubled the advantage following a pass by Wayne Rooney, and the duo combined again as the new club captain made it 3-0 before half-time.
Juan Mata made it four after Di Maria's wayward shot found him free in the area before Radamel Falcao was denied a debut goal of his own by Green late on.
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