The visiting supporters were treated to a goal from Steven Pienaar after only three minutes, as the South African collected a pass from Steven Naismith before firing past Shay Given from 25 yards.
Nikica Jelavic was close to scoring his first goal of the season but his header from close range went wide of Given's post as the Villa fans started to voice their anger at the team's performance.
Villa struggled to recover from the early setback and they moved further ahead in the 31st minute as Marouane Fellaini continued his good form to meet Phil Jagielka's cross with a header.
Jelavic did manage to find a goal before half-time as he took advantage of some woeful defending to finish comfortably from eight yards.
Despite improving slightly after the break, Villa's hopes of an unlikely comeback were destroyed when Ciaran Clark was shown a red card for bringing down Jelavic after the Croatian was put through on goal.
Clark's dismissal didn't change the flow of the match, with Everton still in charge deep into the second half but the hosts did score next as Karim El Ahmadi long-range strike was too much for Tim Howard to keep out.
Everton were rarely troubled after the surprise goal by Villa and were denied a fourth goal when Kevin Mirallas's strike was ruled out for offside.