Richarlison scored twice on his debut but 10-man Everton were left frustrated as Wolves claimed a point on their Premier League return.
The Brazilian winger stabbed home his first from close range, before stroking in a delightful second, BBC reports.
The Toffees had been in control for the opening 40 minutes, but skipper Phil Jagielka was sent off for a dangerous challenge on Diogo Jota.
Wolves levelled at 1-1 from the resulting free-kick with midfielder Ruben Neves curling into the top corner from the edge of the box.
Raul Jimenez struck straight at Jordan Pickford from close range in the second half, but the on-loan Mexican made amends by burying a header with 10 minutes remaining from Neves’ cross.
New Everton boss Marco Silva told BBC Sport: “I don’t have doubts. Even when Richarlison doesn’t score he works really hard to help his team. I’m sure the fans will be proud of him.
“He did very well. He worked hard, which is what I expect from him.”
Richarlison said he was “happy” and would remember the day “the rest of my life”.