The captain's eye-catching goal overshadowed two from Ander Herrera as United climbed into third place above Manchester City, which is at Crystal Palace on Monday.United was leading through Herrera's first-half goal when Rooney used his outstretched left foot to bring down Angel Di Maria's cross and then used his other boot to volley the ball into the net in the 79th minute.
United goalkeeper David de Gea made a rare mistake a minute later, allowing Christian Benteke's shot to go through his legs, but Herrera sidefooted in the third in stoppage time.
Villa is three points above the relegation zone.
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