Steven Naismith marked his Goodison Park debut with a brilliant hat-trick against Greek outfit AEK Athens.
The match also saw Tony Hibbert celebrate his testimonial with his first goal for Everton, but he was overshadowed by new boy Naismith.
The summer signing from Rangers benefited from Steven Pienaar's creativity to put the Toffees in command, first running on to the South African's lofted through-ball to chip over goalkeeper Dimitris Konstantopoulos and then, after Taxiarchis Fountas equalised, heading in a cross to make it 2-1.
The third came from a Pienaar corner after Hibbert's 25-yard effort was tipped over, but the biggest cheer - and a pitch invasion - was reserved for the 53rd minute, when Everton were awarded a free-kick and Leighton Baines teed up Hibbert to drill a low shot under the wall and into the bottom corner.
Sunderland were in action against Derby at Pride Park and they made hard work of a 1-1 draw.
The Black Cats looked set for victory when Kieran Richardson set up James
McClean to put them ahead, but Michael Hoganson, a new signing from Newcastle, crossed for Nathan Tyson to head a late equaliser.
Sunderland's neighbours Middlesbrough also endured a disappointing evening as the Championship outfit lost 3-2 at Scunthorpe United.
Ipswich sealed a win over local rivals Colchester United with a 2-1 win at Weston Homes Community Stadium.