Mario Lemina fired Wolves into the FA Cup quarter final after a nervy 1-0 win over Brighton.
The hosts reached the last eight for just the second time in 21 years and the first time since 2019, when they made the semi-finals.
There is now a path to Wembley for O’Neil’s side, who will host Championship side Coventry in the next round, but they lived dangerously at Molineux.
Facundo Buonanotte wasted a fine opening and goalkeeper Jason Steele, up for a late corner, missed the chance to take the tie extra time.
But last season’s semi-finalists – who dominated for long spells – could not find a way back from conceding the winner after just 77 seconds.
Brighton – missing eight regular starters including Solly March, Joao Pedro, Kaoru Mitoma and James Milner – were already underdogs even before going behind early.
Jean-Ricner Bellegarde’s fine turn sent him scampering away from Jan Paul van Hecke down the left and Steele could only flap at his deflected cross.
Lemina and Pervis Estupinan arrived at the far post, with the Wolves midfielder reacting first to slide the ball in at the second attempt.
But, much like Sunday’s 1-0 Premier League win over Sheffield United, the hosts failed to build on their lead.
Brighton recovered from the shock of the early goal and, with Simon Adingra and Jakub Moder shooting off target, got a grip of the game.
There was little suggestion Wolves would add to their lead, although Steele had to be alert to clear at Bellegarde’s feet after he raced on to Igor’s weak backpass.
It was the Seagulls who created the best openings and they should have levelled seven minutes before the break when Buonanotte planted a free header wide from Estupinan’s cross.
Roberto De Zerbi clearly sensed a way back into the tie and introduced Danny Welbeck at the break, with Brighton continuing to press.
Lewis Dunk nodded wide and Wolves’ frustrations grew when they lost Hwang Hee-chan and Lemina to injury.
Yet the changes, with Pedro Neto and Pablo Sarabia called on, briefly gave the hosts much-needed zip even if they failed to add to a slender lead.
The visitors, though, regrouped again and pinned Wolves back without testing Jose Sa as the game entered its final 15 minutes.
Julio Enciso drilled wide from 25 yards, more in frustration than with a belief he would score, and Welbeck nodded over.
Steele, up for a last-gasp corner, should have taken the tie to extra time but sliced wide from six yards as Wolves squeezed through.
Outgoing Brighton boss De Zerbi not walking into new job
Roberto De Zerbi insisted he does not have another job lined up after overseeing his final game as Brighton and Hove Albion boss on Sunday.
One day after surprisingly announcing De Zerbi's departure, Brighton ended their Premier League campaign with a 2-0 home loss to Manchester United.
That meant they slipped below rivals Crystal Palace to finish 11th in the table, their first bottom-half placing since finishing 16th in 2020-21.
De Zerbi has been linked with several big clubs since leading Brighton to European qualification last season, with Bayern Munich, Milan and Napoli touted as possible landing spots for the former Sassuolo and Shakhtar Donetsk coach.
However, De Zerbi says he has not reached an agreement with any other club, telling reporters: "There isn't any club – no-one offered me anything. At the moment, nothing.
"I hope to work in the Premier League again. I don't know where or when, but it was an honour to work in the Premier League."
Sunday's defeat was De Zerbi's 70th Premier League game in charge of Brighton, with his top-flight win percentage of 37 per cent (26/70) the highest of any boss in the Seagulls' history.
Battling a lengthy injury list for much of 2023-24, Brighton made a total of 143 changes to their starting lineup throughout the course of the campaign, with only Manchester City in 2019-20 (144) ever making more in a single Premier League season.
Asked by BBC Match of the Day if there was a particular reason for his exit, the Italian added: "We didn't find the agreement to move on. I want to keep my way.
"I know very well what I want to do and I know I am a coach and I have to accept the policies of the club.
"They gave me an incredible chance. They gave me the possibility to know incredible people, to play and to work in the Premier League, to play in the Europa League. They gave me the opportunity to know this club, this city, these fans and that I cannot forget."
Ipswich Town boss Kieran McKenna and Nice coach Francesco Farioli have both been tipped as possible contenders to replace De Zerbi, with Brighton having a reputation for excellent succession planning under owner Tony Bloom.
Asked about the search for a replacement on Sunday, Bloom said: "We always try and have a plan. We have got a plan. We now need to execute that plan."
Walker: Man City driven on by creating history
Kyle Walker believes Manchester City were spurred on by creating history to a fourth straight Premier League title.
A Phil Foden double and a Rodri strike saw City beat West Ham 3-1 on Sunday as they claimed a fourth consecutive Premier League crown, finishing two points above Arsenal.
In doing so, City became the first team ever to win England's top division four times in a row, and Walker feels that was one of the key motivations behind the team finishing top of the Premier League pile yet again.
When asked if creating history had driven him and his team-mates on, Walker told Sky Sports: "I think so, I think so. We went out of the Champions League, got into the FA Cup final, but to do this, make it four in a row, it made it something special.
"It has been spoken about all year what we can achieve and the history we can make. But it is about the finer details. It was down to just one game and that game was West Ham United. We get past that then we make history, but more importantly we claim the Premier League again.
"It is a very, very tough league to win. I looked at the Italian league, German league, Spanish league, the winners are 10, 15 points clear. Fair play to Arsenal and Liverpool for what they have done throughout the season, making sure they push us right to the limit."
Walker turns 34 later this month but has shown little signs of slowing down, playing an integral role again this season on his way to a sixth Premier League title of his decorated career.
Walker still feels he is capable of playing at the top level, saying: "I feel young. I don't know if that is a good thing or a bad thing. I feel young, I feel great, I still have my pace.
"I come to training every day wanting to learn. Once that goes then it is probably time to pack up, but this group of lads keeps you on your toes. They keep on you to keep improving every day."
Walker has been City's captain this season, making his 300th appearance for the club in the title-securing win over West Ham.
The defender was keen to emphasise that it has been a collective effort this term, though, explaining: "I am the man at the front and I wear the armband, but I don't put myself above anyone else. We are a team.
"There are four captains including myself, and we all pull our weight. I am just the man they've picked to wear the armband which I am very grateful for. To be able to lift the trophy in this scenario, the four in a row, it is a dream come true."
Ancelotti focused on fitness and rhythm despite Villarreal comeback against Madrid
Carlo Ancelotti was unbothered by Real Madrid's failed attempt to defend a three-goal lead against Villarreal, instead focusing on avoiding injuries and keeping their rhythm.
A double from Arda Guler, as well as goals from Joselu and Lucas Vazquez, had Madrid in control at 4-1 up away to Villarreal on Sunday.
Yet Alexander Sorloth, who pulled a goal back earlier on, managed three goals in eight minutes to salvage a 4-4 draw for the hosts against the LaLiga champions.
Despite faltering to a late comeback, Ancelotti was more than pleased with his side's efforts, ahead of the upcoming Champions League final with Borussia Dortmund on June 1 at Wembley Stadium.
"The target was not the points because we don't need them, the target was to play a good game with rhythm, intensity, avoiding injuries. Everything went perfectly," he told a post-match press conference.
"I'm not worried ahead of the Champions League final, this was an open game.
"Maybe we conceded more goals than necessary but that's okay, it doesn't change anything about what the final has to be. In attack, we played well."
Villarreal are set to finish eighth in the LaLiga table, unable to be caught by any team below and incapable of reaching seventh-placed Real Betis.
Sorloth may end with an individual award, though, after scoring his league-leading 23rd goal of the season with the fourth of his quartet of strikes.
"It was a match with a lot of goals, the kind that the fans like," Villarreal forward Gerard Moreno, who provided three assists, told Movistar.
"I'll take the reaction in the second half. We will try to go to Europe next year.
"I hope Sorloth ends up top scorer. He's a fantastic teammate. He deserves it. We're going to try to help him. He's had an incredible season."
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