United dominated the opening 45 minutes despite the early loss of Mexico striker Javier Hernandez with a left ankle injury.
Jones scored in the 20th, picking up a cross from Nani on the left and deftly side-footing a close-range volley through Villa goalkeeper Shay Given.
It was Jones’ first goal in any competition for United since his summer move from Blackburn.
Villa has won just one of the last 32 league matches against United.
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