Steven Pienaar, Marouane Fellaini and Nikica Jelavic all scored as Paul Lambert suffered a nightmare first home league game in charge of Aston Villa.
Pienaar's delightful 20-yard finish set Everton on their way and they doubled the lead after keeper Shay Given's mistake allowed Fellaini to score.
Lambert blames 'poor start' for defeat
Everton added a third before half-time when Jelavic netted from close range.
Villa, who had Ciaran Clark sent off for a foul on Jelavic, grabbed a consolation through Karim El Ahmadi.
While Everton are now unbeaten in 11 Premier League games stretching back to March, problems are mounting at Villa after they lost their opening two Premier League games of the season for the first time since the 2002-03 campaign.
They finished 16th in the table back then, and another long season appears to be on the cards for the West Midlands club after Lambert saw his team outclassed and outfought by the determined visitors.
Lambert has been busy in the transfer market since his appointment - Villa signing Ron Vlaar, Matthew Lowton, Brett Holman and El Ahmadi during the summer.
But it is a case of new faces, same old story.
Red mist for Aston Villa
Ciaran Clark's red card was Aston Villa's first since Alan Hutton was given his marching orders in a 2-1 home defeat to Arsenal on 21 December 2011.
Everton were everything Villa were not - bright, hungry, sharp and creative.
Not only did Fellaini score his second goal in as many games, Pienaar scored his first since re-signing from Tottenham last month, while Jelavic now has 10 goals in 15 Premier League appearances.
But there were telling contributions from Leighton Baines and Phil Neville, the full-backs eager to get forward at every opportunity to supply the ammunition for Fellaini, Pienaar and Jelavic.
There was only one winner once Pienaar opened the scoring with a stylish fourth-minute finish, a delightful 20-yard attempt beyond Given after Steven Naismith's clever lay-off.
Jelavic twice spurned good opportunities before Fellaini doubled the lead in the 32nd minute after Phil Jagielka's cross, Given allowing the ball to squirm past him when he should have done much better.
Moyes hails Everton's unbeaten start
Villa managed just one shot on target in the first half - Barry Bannan testing Tim Howard - but Everton were already 3-0 ahead after Jelavic's 44th minute close range finish following good work by Baines.
It was damage limitation for Villa long before Clark was shown a straight red for bringing down Jelavic, and they were forced to play for more than half an hour with only 10 men.
Everton, who introduced new signing Kevin Mirallas from the substitutes' bench in the closing stages, were denied a fourth goal when Bent cleared off the line from Sylvain Distin.
But Villa finished strongly, El Ahmadi firing his new team's first goal of the season in the 75th minute with a curling finish before Andreas Weimann hit the post in injury time.
Full Time The referee signals the end of the game.
Brett Holman produces a left-footed shot from inside the area that clears the bar.
Leon Osman takes a shot. Comfortable save by Shay Given.
Andreas Weimann has an effort at goal from deep inside the box striking the post. Darren Bent takes a shot. Leighton Baines gets a block in. Charles N'Zogbia takes a short corner.
The ball is crossed by Seamus Coleman. Kevin Mirallas is flagged offside by the assistant referee. Shay Given takes the free kick.
Substitution Johnny Heitinga comes on in place of Nikica Jelavic.
Kevin Mirallas takes a shot. Ron Vlaar gets a block in.
Effort from the edge of the box by Nikica Jelavic goes wide of the right-hand upright.
Leon Osman restarts play with the free kick.
Booking Karim El Ahmadi is booked.
Leon Osman fouled by Karim El Ahmadi, the ref awards a free kick.
Matthew Lowton fouled by Leighton Baines, the ref awards a free kick. Direct free kick taken by Matthew Lowton.
Shot from just outside the penalty area by Eric Lichaj misses to the left of the target.
Assist by Eric Lichaj.
73:53 Goal scored
Goal! - Karim El Ahmadi - A Villa 1 - 3 Everton Karim El Ahmadi finds the net with a goal from long distance to the bottom right corner of the goal. Aston Villa 1-3 Everton.
Foul by Steven Pienaar on Matthew Lowton, free kick awarded. Direct free kick taken by Ron Vlaar.
Corner taken by Leighton Baines.
Substitution (Everton) makes a substitution, with Kevin Mirallas coming on for Darron Gibson.
Substitution Barry Bannan goes off and Andreas Weimann comes on.
Seamus Coleman takes the outswinging corner, Matthew Lowton makes a clearance. Corner taken by Leighton Baines from the left by-line, Darron Gibson takes a shot. Blocked by Nathan Baker.
Seamus Coleman produces a cross.
Free kick awarded for an unfair challenge on Leighton Baines by Matthew Lowton. Leighton Baines takes the direct free kick. A cross is delivered by Darron Gibson, clearance by Ron Vlaar.
Darron Gibson restarts play with the free kick. Save by Shay Given.
Substitution Seamus Coleman replaces Steven Naismith.
Unfair challenge on Marouane Fellaini by Karim El Ahmadi results in a free kick. Darron Gibson takes the direct free kick. A cross is delivered by Leighton Baines, Steven Pienaar takes a shot. Save by Shay Given. Corner taken left-footed by Leighton Baines from the left by-line, Sylvain Distin takes a shot. Phil Jagielka fouled by Brett Holman, the ref awards a free kick.
Charles N'Zogbia fouled by Steven Naismith, the ref awards a free kick. Shay Given takes the direct free kick.
Substitution Eric Lichaj joins the action as a substitute, replacing Chris Herd.
Strike on goal comes in from Darron Gibson from the free kick.
Dismissal Ciaran Clark shown a red card.
Ciaran Clark challenges Nikica Jelavic unfairly and gives away a free kick.
Handball by Marouane Fellaini. Nathan Baker takes the direct free kick.
Matthew Lowton crosses the ball, Leighton Baines manages to make a clearance. Barry Bannan takes a shot. Darron Gibson gets a block in. Unfair challenge on Nathan Baker by Marouane Fellaini results in a free kick. Nathan Baker restarts play with the free kick.
Outswinging corner taken left-footed by Leighton Baines from the left by-line. The ball is swung over by Leighton Baines, Headed effort from inside the box by Sylvain Distin misses to the right of the target.
Darron Gibson has an effort at goal from just outside the box which goes wide of the right-hand post.
Nikica Jelavic takes a shot. Blocked by Ciaran Clark. Outswinging corner taken from the right by-line by Darron Gibson, Darren Bent manages to make a clearance.
The referee starts the second half.
Substitution Brett Holman on for Nathan Delfouneso.
45:00 +1:11 Half time
Half Time The whistle is blown to end the first half.
Barry Bannan takes a shot. Save by Tim Howard.
The assist for the goal came from Leighton Baines.
42:59 Goal scored
Goal! - Nikica Jelavic - A Villa 0 - 3 Everton Nikica Jelavic finds the back of the net with a goal from deep inside the penalty box to the top left corner of the goal. Aston Villa 0-3 Everton.
Marouane Fellaini takes a shot. Barry Bannan gets a block in.
Nikica Jelavic is adjudged to have handled the ball. Free kick taken by Shay Given.
Phil Jagielka challenges Charles N'Zogbia unfairly and gives away a free kick. Free kick taken by Nathan Baker.
Effort on goal by Phil Jagielka from inside the penalty box misses to the right of the target.
Assist by Phil Jagielka.
30:21 Goal scored
Goal! - Marouane Fellaini - A Villa 0 - 2 Everton Marouane Fellaini grabs a headed goal from inside the box. Aston Villa 0-2 Everton.
Marouane Fellaini concedes a free kick for a foul on Chris Herd. The free kick is delivered left-footed by Barry Bannan from right wing, save by Tim Howard.
Marouane Fellaini handles the ball and concedes a free kick. Barry Bannan delivers the ball from the free kick left-footed from right wing.
Phil Neville challenges Charles N'Zogbia unfairly and gives away a free kick. The free kick is swung in left-footed by Charles N'Zogbia, Darron Gibson makes a clearance.
Leon Osman takes a shot. Ron Vlaar gets a block in. Effort on goal by Darron Gibson from long range goes harmlessly over the target.
Nathan Delfouneso sends in a cross, clearance by Sylvain Distin.
The assistant referee signals for offside against Steven Pienaar. Indirect free kick taken by Shay Given.
Inswinging corner taken left-footed by Leighton Baines played to the near post, Nikica Jelavic has a headed effort from close range and clears the crossbar.
Nathan Baker gives away a free kick for an unfair challenge on Steven Naismith. Direct free kick taken by Darron Gibson.
Karim El Ahmadi concedes a free kick for a foul on Leon Osman. Steven Pienaar restarts play with the free kick.
Unfair challenge on Steven Naismith by Karim El Ahmadi results in a free kick. Free kick taken by Darron Gibson.
Darron Gibson takes the outswinging corner, clearance by Chris Herd.
Unfair challenge on Steven Naismith by Ciaran Clark results in a free kick. Direct free kick taken by Darron Gibson.
The ball is delivered by Leighton Baines, Nikica Jelavic produces a header from deep inside the six-yard box that clears the crossbar.
Leighton Baines takes the outswinging corner, Nathan Delfouneso makes a clearance.
Unfair challenge on Marouane Fellaini by Ron Vlaar results in a free kick. Direct free kick taken by Darron Gibson.
Steven Pienaar sends in a cross.
The assist for the goal came from Steven Naismith.
2:32 Goal scored
Goal! - Steven Pienaar - A Villa 0 - 1 Everton Steven Pienaar gets on the score sheet with a goal from just outside the box to the top right corner of the goal. Aston Villa 0-1 Everton.
Nikica Jelavic delivers the ball, Ciaran Clark makes a clearance.
The ball is crossed by Nathan Delfouneso, Leon Osman makes a clearance.
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