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.
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”.
Wolves spoil Richarlison-Silva reunion
Silva was linked with a move to Goodison Park last season but Everton appointed Sam Allardyce instead, who oversaw an eighth-place finish.
Silva was sacked by Watford in January with the Hornets blaming Everton’s interest for a downturn in form. The Toffees finally got their man this summer after dismissing Allardyce.
The Portuguese’s first signing was Richarlison from his former club and much was made about the potential £50m fee, particularly having not scored for Watford since last November.
But it looks to be a shrewd move by Silva to link up again with the 21-year-old, who displayed his qualities inside and outside the box.
Playing from the left, he posed a dangerous threat to Wolves wing-back Matt Doherty and his 13 sprints during his 86 minutes on the pitch was bettered only by team-mate Seamus Coleman (15).
Richarlison opened the scoring with a opportunistic strike as Wolves failed to clear a Leighton Baines free-kick into the box, while his second was a measured finish into the far corner.
He also came close to making a goal when his knockdown fell nicely in the box for Theo Walcott, but the former Arsenal man’s scuffed shot failed to threaten Rui Patricio.
Richarlison added: “I have to thank my colleagues because we had to run double with one player less, so it is a special day for me.”
Everton would have been in a better position to claim all three points had Jagielka not been dismissed after losing control of the ball deep in his own half and catching Jota on the shin in trying recover possession.
“Phil Jagielka’s red card was a harsh decision,” said Silva. “Not only the red card but they scored from the free-kick.”
Battling Wolves impress on return
Wolves won the Championship with ease last season, claiming 99 points as they returned to the top flight for the first time since the 2011-12 campaign, when they finished bottom.
They spent big money in the summer on eight recruits, helped by agent Jorge Mendes’ contacts, including the signings of former Sporting Lisbon goalkeeper Patricio and international team-mate Joao Moutinho from Monaco.
In all, Portuguese manager Nuno Espirito Santos fielded five compatriots – the most by any Premier League club – and he will be pleased by the fighting spirit shown by his team.
Although they struggled to impose themselves on the game early on, Wolves battled back to earn a point on a day when fellow promoted sides Fulham and Cardiff went down to 2-0 defeats.
Nuno said: “We have character because we came back from a goal down twice, which is not easy.
“Today taught me that we can react to goals but we have a lot to improve. We have always known we have quality but we are in a growing process. It was the first time for a lot of us in the Premier League but we will get better and better.”
Ex-Porto captain Neves was one of the best players in the Championship last season and he impressed on his step up by scoring one goal and making the other.
He looked comfortable in possession too – his 111 touches on the ball and 93 passes were more than any other player on the pitch – and he contributed defensively by winning the ball back six times.
Neves said: “I am very happy to help the team achieve a point but we want to win games, mainly at home.”
Wolves have been tipped by many pundits to claim a top-half finish this season and they could well achieve that target after making a promising start to the new campaign.
Man of the match – Ruben Neves (Wolves)
Wolves player’s long wait – the stats
- Wolves are now seven league matches without a victory against Everton (D5 L2) since a 2-1 win in May 2004.
- Everton have drawn their past three opening day Premier League matches against newly promoted sides, also doing so in 2014-15 against Leicester City and 2015-16 against Watford – all finished 2-2.
- Richarlison found the net with his first two shots in the Premier League for Everton, having failed to score with any of his last 53 shots as a Watford player.
- Since the start of last season, Wolves midfielder Ruben Neves has scored more goals from outside the box than any other player in the top four tiers of English league football (seven).
- Everton’s red card was their 90th in the Premier League – more than any other side.
- Wolves defender Matt Doherty made his second Premier League appearance – 2,513 days after his first in September 2011; only two outfield players have had a longer wait for their second appearances – Erik Nevland (3,667) and Darren Pratley (2,835).