Tony Hibbert celebrated his testimonial match with his first goal for Everton while new boy Steven Naismith hit a hat-trick in a 4-1 win over AEK Athens.
Naismith, a 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 Pienaar 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 also in action as they had to settle for a 1-1 draw against Championship side Derby County at Pride Park.
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.