Steven Pienaar's spectacular strike after just three minutes left Paul Lambert's side trailing from virtually the get-go, and an eventual spell of Villa control was soon killed off by Marouane Fellaini's second of the season with half an hour played.
Nikica Jelavic added to Villa's miseries just before half-time with the third, and a straight red card for Ciaran Clark early in the second period capped another miserable home fixture for season-ticket holders.
The Midlanders were able to finish on something of a positive note, however, as a stunning distance drive from Karim El Ahmadi was followed by substitute Andreas Weimann hitting the post in the closing stages.
But the Toffees now have their first three points from Villa Park since the 2004-05 season, when they went on to finish fourth. And after defeating Manchester United on opening day and shattering their habit of slow league starts, European football will appear a viable expectation on the blue half of Merseyside.
Villa began the season with a 1-0 defeat at West Ham but would have relished the opportunity to get their campaign properly started on home turf.
They were in for a fast wake-up call, however, when after Nathan Delfouneso had threatened in the opening moments with good play on the right wing, the Toffees went straight up the other end and broke the deadlock with just three minutes played.
Steven Naismith, who had only just helped clear Delfouneso’s cross inside his own area, soon found himself on the edge of Villa’s to tee up a superb 25-yard drive from Pienaar for his first goal since returning to the fold after a brief stint at Tottenham.
It took the home team another 15 minutes to settle into the game, though even when they did finally start stringing together passes and controlling possession meaningful attempts on goal remained elusive.
With a shade over half an hour on the clock Everton broke away from the growing pressure and doubled their advantage, with Phil Jagielka of all people producing a brilliant first-time delivery from the right wing, which a poorly-marked Fellaini powered home for his second headed goal in two games.
The second goal deflated the home players and fans, with Everton continuing to pick their hosts apart and claiming a third with two minutes remaining in the half.
Leighton Baines, whose set piece deliveries had kept Villa on their toes throughout the opening period, cut the ball back from the left to Jelavic whose assured finish across Shay Given heaped further misery on Paul Lambert’s side.
Everton were not happy with just the three and started the second 45 brightly, with only an excellent Nathan Baker sliding intervention denying Jelavic a second.
The Croatian continued to torment on 57 minutes when an inch-perfect sliding through pass from Darron Gibson put him clean through and forced a foul from Clark which earned the defender a straight red card.
It was Gibson who took the resulting free-kick as Lambert scrambled together plans to bring another defender on, and the former Manchester United man came close to adding a fourth, shooting inches over the bar.
Baines provided another potentially dangerous cut-back on 63 minutes when he picked out Pienaar, whose half-volley forced a great reaction from Given to tip it over. The subsequent corner was headed towards goal by Sylvain Distin, with Darren Bent on the line to deflect it onto the bar before the danger was cleared.
Kevin Mirallas was introduced for the first time on 71 minutes in place of Gibson, and almost scored with his first touch in an Everton shirt but for Ron Vlaar crucially intercepting a Seamus Coleman cross.
The visitors began to coast on their lead soon after, allowing Villa restore just a shred of pride with their finish.
El Ahmadi found space 30 yards out to unleash a powerful drive 16 minutes from time which finally gave the occupants of the home stands something to cheer, though Tim Howard should have done better in trying to keep the ball out of goal.
And after Mirallas was denied a debut goal by the offside flag with two minutes remaining, Weimann almost provoked a tense finish when his effort in the dying embers crashed off the upright.
