Richarlison, Everton's record signing, scored twice on his debut as their 10 men drew 2-2 away to Premier League new boys Wolves.
The £50 million Brazilian, bought from Watford, scored his first brace in English football as Marco Silva's side survived the 41st-minute dismissal of captain Phil Jagielka.
Ruben Neves was the standout performer for Wolves, scoring their first equaliser with a stunning free kick, then setting up Mexican striker Raul Jimenez's header.
The Molineux men started four of their 10 summer signings, 2281 days after the club's last appearance in the top flight, in May 2012.
Rui Patricio, Jonny Castro Otto, Joao Moutinho and Jimenez made their competitive debuts, while Willy Boly and Diogo Jota were playing for the first time since their season-long loans were made permanent.