After their 1-0 victory over Manchester United last week, the Toffees stunned their opponents with a goal from Steven Pienaar after just three minutes, before Marouane Fellaini added a second on the half-hour mark.
Nikica Jelavic struck a third just before the break and Ciaran Clark was sent off for Villa, and although the home side pulled one back through Karim El Ahmadi, it was a comfortable win for the visitors.
|TOFFEES COME UNSTUCK
|17/2||West Brom are 17/2 with Paddy Power to beat Everton 2-1 next Saturday|
"The performance was excellent. It was up there with a lot of the really good performances I've had at Everton," Moyes told Sky Sports after the game.
"I've got to give great credit to the players. They went out and showed today the confidence they've taken from the result last week."
He also praised the influence of Pienaar, who returned to the club permanently this summer after a successful loan spell from Tottenham, for whom he signed from Goodison Park in January 2011.
"It was massive with the way he [Pienaar] played for us at the end of last season," Moyes explained.
"He was key to a lot of things we did. The players enjoyed playing with him. His general play today was excellent - throughout the game he was fantastic."