First-half goals from Yoseph Yobo, Sylvain Distin and Steven Pienaar did most of the damage, before Jo set the seal on the easy victory with a late fourth.
However, Louis Saha's stoppage-time sending off took the gloss of what had been an impressive team performance.
The Toffees have started the Premier League season in sticky fashion after winning just one of their opening four games.
However, from the pre-match announcement that they had completed the signing of free agent former Blackburn Rovers and West Ham United defender Lucas Neill, there was an upbeat atmosphere around Goodison Park.
Toffees boss David Moyes made three changes to the side that lost 2-1 at Fulham on Sunday with Diniyar Bilyaletdinov handed a first start and Marouane Fellaini and Dan Gosling in for the injured Phil Neville and suspended Tony Hibbert.
The home side started quickly and, after a series of dangerous raids, it was no surprise when they took the lead after just 10 minutes.
Pienaar's 30-yard shot was saved but when Bilyaletdinov returned the ball from the corner, it fell to the unmarked Yobo who nodded home in acres of space at the back post.
Seven minutes later it was 2-0 as Distin claimed his first goal for the club since arriving in the transfer window from Portsmouth.
Fellaini got a slight touch to another Bilyaletdinov corner and Distin prodded the ball over the line from close range.
Everton looked dangerous every time they were in possession with Pienaar and Bilyaletdinov a constant menace down the flanks.
It was little surprise when the diminutive South African crashed home the third goal of the night on 37 minutes when he let fly with a thumping shot from 25 yards.
Moyes replaced Tim Cahill and Bilyaletdinov with the game effectively over and the former on a yellow card and the latter carrying a groin injury.
Any hopes the visitors had of clawing their way back into the match were ended with the 55th minute red card shown to Luciano Carlos Araujo for a petulant flick out at Distin.
Pienaar and Jack Rodwell brought good saves out of goalkeeper Diego Saja with low shots as Everton kept their foot on the gas.
Substitute Leon Osman drilled a volley wide of the target despite the pace of the game visibly slowing in the final third of the match.
The margin of victory should have been greater with substitute Saha guilty of the worst miss when he stabbed over from close range following a Leighton Baines cut-back on 80 minutes.
Jo did make it 4-0 soon after when Ayegbeni Yakubu stumbled his way into the box and the Brazilian lashed a shot on the turn past the helpless keeper.
But the game ended on a sour note for the Toffees when Saha was red-carded in stoppage time after needlessly raising his hand to AEK defender Juanfran following a tussle between the pair in the penalty area.