The Toffees confirmed the appointment of new manager Carlo Ancelotti just an hour before kick-off but it was interim boss Duncan Ferguson who continued in the dugout.
Arsenal had revealed their own new manager on Friday, with Mikel Arteta leaving his coaching role at Manchester City to replace Unai Emery as permanent Gunners boss.
Both men will now know they have plenty of work to do after watching from the stands at Goodison Park.
After a slow start to the game, Everton midfielder Gylfi Sigurdsson had some of the supporters thinking he had opened the scoring as his free-kick went close before ruffling the side-netting.
In a first half of low quality and few opportunities, Arsenal’s Gabriel Martinelli had a great chance just before the break when he worked himself some space before slicing his shot wide.
Pierre-Emerick Aubameyang had a chance in the 52nd minute when he found himself free at the back post from a corner but failed to get a clean strike away, with his effort palmed away by keeper Jordan Pickford.
In the 70th minute Everton had appeals for a penalty waved away after Dominic Calvert-Lewin’s shot was blocked, seemingly by the hand of Lucas Torreira, but no action was taken by referee Kevin Friend.
Neither side could find a breakthrough and a sense of relief was felt all around Goodison Park when the full-time whistle finally went.