Match ends, Wolverhampton Wanderers 2, Everton 2.
Everton manager Marco Silva said he "doesn't have doubts" about Richarlison after the big money summer signing scored twice on his debut in an entertaining draw at Premier League newcomers Wolves.
The Toffees - reduced to 10 men at the end of the first half when Phil Jagielka was sent off for a dangerous challenge on Diogo Jota - were left frustrated as Wolves twice fought back to claim a point.
The potential £50m signing of Brazilian winger Richarlison raised eyebrows in the summer, particularly since he endured a run of 28 games without a goal in 2017-18, last finding the net in November.
But he repaid his manager's faith when he stabbed home his first from close range, before stroking in a delightful second to restore the lead.
Ruben Neves' free kick - from the tackle which saw Jagielka sent off - had brought Wolves level, and they eventually rescued a point when on-loan Benfica forward Raul Jimenez buried a header from Neves' cross with 10 minutes remaining.
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 would remember the day for "the rest of my life".
- Chelsea off to flying start as newcomers fail to win - Premier League round-up
- Relive the draw at Molineux
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 fee.
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 an 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, manager Nuno Espirito Santo fielded five of his Portuguese compatriots - a Premier League record - 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.
Jagielka challenge 'endangered' Jota
BBC Match of the Day pundit Alan Shearer
I thought it [Phil Jagielka's red card] was the correct decision. It's a poor touch he knows he's in trouble. It's endangered Diogo Jota and there's not too much argument.
He uses excessive force and he's out of control. It's a straight leg and a red card. Whether you agree with the laws or not, that's the law.
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).
- 11Rui Patrício
- 28João MoutinhoSubstituted forGibbs-Whiteat 85'minutes
- 19Castro OttoSubstituted forVinagreat 76'minutes
- 10Hélder CostaSubstituted forBonatiniat 71'minutes
- 6JagielkaBooked at 40mins
- 10G SigurdssonSubstituted forHolgateat 43'minutes
- 30RicharlisonBooked at 14minsSubstituted forDigneat 86'minutes
- 14TosunSubstituted forNiasseat 81'minutes
- Craig Pawson
- Shots on Target
Second Half ends, Wolverhampton Wanderers 2, Everton 2.
Attempt missed. Diogo Jota (Wolverhampton Wanderers) right footed shot from outside the box is too high. Assisted by Ryan Bennett.
Foul by Diogo Jota (Wolverhampton Wanderers).
Morgan Schneiderlin (Everton) wins a free kick in the defensive half.
Rúben Neves (Wolverhampton Wanderers) wins a free kick in the defensive half.
Foul by Lucas Digne (Everton).
Offside, Wolverhampton Wanderers. Morgan Gibbs-White tries a through ball, but Raúl Jiménez is caught offside.
Delay over. They are ready to continue.
Substitution, Everton. Lucas Digne replaces Richarlison because of an injury.
Delay in match Richarlison (Everton) because of an injury.
Substitution, Wolverhampton Wanderers. Morgan Gibbs-White replaces João Moutinho.
Substitution, Everton. Oumar Niasse replaces Cenk Tosun.
Goal! Wolverhampton Wanderers 2, Everton 2. Raúl Jiménez (Wolverhampton Wanderers) header from the centre of the box to the bottom right corner. Assisted by Rúben Neves with a cross.
Corner, Wolverhampton Wanderers. Conceded by Michael Keane.
Attempt blocked. Raúl Jiménez (Wolverhampton Wanderers) right footed shot from the centre of the box is blocked. Assisted by Matt Doherty with a cross.
Rúben Neves (Wolverhampton Wanderers) wins a free kick in the defensive half.
Foul by Morgan Schneiderlin (Everton).
Substitution, Wolverhampton Wanderers. Rúben Vinagre replaces Jonny.
Attempt missed. Jonny (Wolverhampton Wanderers) right footed shot from outside the box is high and wide to the right.