Steven Pienaar kicked things off early with a brilliant finish to put the Toffees a goal up inside three minutes, curling his effort into Shay Given's top left corner from outside the area.
The second Everton goal came just after the half-hour mark when Marouane Fellaini, who destroyed United on Monday night, again rose above his marker to send a powerful header home from Phil Jagielka's rightwing cross although Given should have a lot better.
The contest was effectively over two minutes before half-time when Leighton Baines advanced down the left before producing a nice cutback pass for Nikica Jelavic to finish with a first-time effort across his body to open his account for the season.
Just prior to the hour-mark, Villa were reduced to ten men when Ciaran Clark was sent off for pulling down Jelavic as the last defender, making life much more difficult for the home team.
Villa did manage to get one back with just over 15 minutes through summer signing Karim El Ahmadi who received a pass from Eric Lichaj, before hammering it past Tim Howard from 25 yards, but unfortunately for Paul Lambert's side, the damage had been done.
Villa Park, Birmingham - 36,565
Yellow cards:AV - Karim El Ahmadi 81' EVE - nil
Red card:AV - Ciaran Clark 58'