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.
Wolves had five Portuguese players in their team - Patricio, Moutinho, Neves, Helder Costa and Jota - a Premier League record.
Everton included only Richarlison of their six senior new arrivals, with Lucas Digne on the bench and Kurt Zouma, Yerry Mina, Bernard and Andre Gomes not considered ready.
Richarlison was perfectly placed to prod home the opening goal in the 17th minute after Boly and Cenk Tosun had tussled in the air for Leighton Baines' free kick and the loose ball bounced off Boly.
Nuno Espirito Santo's side were given the chance to haul themselves back in the game four minutes before the break when Jagielka was sent off.
The former England defender had a poor first touch from a pass across the back which allowed Jota to dart in. Jagielka brought him down with a lunging challenge which caught the Portuguese around the shins and referee Craig Pawson had no hesitation in quickly producing a red card.
Neves unleashed a superb, curling effort into the top corner of the net from the resulting free kick 20m out to bring Wolves level and almost lift the roof off Molineux.
Everton regained the lead in the 67th minute with another goal from Richarlison. This time, the 21-year-old ran away from Neves on to a short, square pass from Tosun before neatly curling the ball beyond Patricio.
Wolves remained composed, however, and continued to probe for a second equaliser. And they were rewarded with another quality goal in which Neves had a heavy influence 10 minutes from time.
The playmaker dug out a sublime, pacy cross which just needed the slightest touch from Jimenez to send it flying high into the net, again giving keeper Jordan Pickford no chance.