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.