Referee Phil Dowd incensed Villa by not sending Vidic off, and didn't even produce a yellow card for the Serbian.
Owen looked sharp all afternoon and troubled the Villa defence constantly, but his afternoon ended early as he injured his hamstring.
His replacement Rooney scored the winner with 16 minutes remaining after Ji-Sung Park had earlier hit a post for the Old Trafford outfit.
Antonio Valencia crossed and the England striker headed powerfully into the top corner.
Rooney almost got a second as another header this time hit the woodwork but Villa were just as unlucky when Stuart Downing's cross took a deflection of Vidic and hit the cross bar.