Tim Cahill scored on his return from injury as Everton saw off Greek side Larissa in their opening Group A clash.
Cahill lasted 65 minutes for Everton
Playing his first competitive game for the Toffees since March, Cahill headed the hosts in front after Leon Osman's fierce cross from the left.
Leighton Baines and Steven Pienaar combined well down the left to tee up Osman who drilled in a sublime second.
Silva Cleyton punished Joleon Lescott's mistake for Larissa but Victor Anichebe sealed it with a fine run and finish.
Anichebe's late strike settled the nerves after a late fightback from the visitors but it was Cahill's early goal that set up this comfortable victory.
The midfielder was superb throughout his 65-minute run-out and gave Everton's midfield a edge that had been missing since he broke his metatarsal against Sheffield United last season.
His energy in midfield rallied David Moyes' side who looked to be struggling with their changed 4-5-1 formation early on.
And on his 100th appearance for the club, he dived to head Osman's fierce cross past the helpless Stefanos Kotsolis on 14 minutes.
The goal settled the home side who had looked cagey in the opening stages. Cahill and Mikel Arteta subsequently sparked Everton into life with Spaniard Arteta providing dangerous set-pieces and Cahill a constant menace in the centre.
The Australian international almost smashed a second shortly before the break with a crisp drive from 30 yards that was well palmed away by Stefanos Kotsolis.
Georgios Fotakis cracked a meaty drive from 25 yards out in Larissa's best chance of the first half, but Tim Howard's most meaningful duties were claiming hopeful balls pumped into his box.
Osman drives home Everton's second
James McFadden wasted a glorious chance to double the lead immediately after the break after being put clean through by Lescott. His shot found the keeper's sprawling legs when he should have put Everton firmly in charge.
And he would have been relieved to see Osman do just that minutes later.
Baines burst down the left and crossed for Pienaar whose neat flick found the onrushing Osman who crashed home a sweet strike which left the keeper rooted to the spot.
Cleyton, who scored two goals in the previous round to oust Blackburn, gave Larissa hope with a well-taken goal on 65 minutes.
He took advantage of Lescott's indecision on the edge of the box and after jinking past Joseph Yobo, he drove neatly past Howard.
That stirred the Greeks who caused moments of concern for Moyes in the final 20 minutes.
But Anichebe turned the nervous situation into one of relief when he held off two challenges to steer home from 12 yards.
Everton boss David Moyes:
"I thought the goals we scored were really good and getting Cahill back and Thomas Gravesen was a bonus," he said.
"Scoring is what Tim does for us and he has been doing it for years. He did again and you see what it means to him.
"It is a big thing for our squad and thankfully he is back and come through it with no problems. It will benefit him in the coming weeks."
Everton: Howard, Hibbert, Yobo, Lescott, Baines, Pienaar (Stubbs 87), Osman, Carsley, Cahill (Gravesen 65), Arteta, McFadden (Anichebe 65).
Subs Not Used: Wessels, Jagielka, Yakubu, Nuno Valente.
Booked: Lescott, Yobo, Gravesen.
Goals: Cahill 14, Osman 50, Anichebe 85.
Larissa: Kotsolis, Galitsios, Foerster (Venetis 79), Dabizas, Venetidis, Cleyton, Fotakis, Kiriakidis (Labropoulos 75), Sarmiento, Parra (Kalantzis 58), Bakayoko.
Subs Not Used: Kipouros, Kotsios, Gikas, Katsiaros.
Goals: Cleyton 65.
Ref: Martin Ingvarsson (Sweden).