Ivan Cavaleiro's first-half strike was the difference as Wolves narrowly beat Bristol City 1-0 at Ashton Gate to progress to the FA Cup quarter-finals.
The 25-year-old forward met Matt Doherty's squared pass to hand Wolves a deserved lead in the 28th minute, and the latter almost made it two moments later when his strike smashed off the inside of the post.
City changed to a three-man defence in the second half with substitutes Matty Taylor and Marlon Pack both squandering good goal-scoring opportunities.
But the Premier League side held on, with Frank Fielding denied by opposing goalkeeper John Ruddy in added time, to reach the last eight for the first time in 16 years.
Wolves will find out their next opponents on Monday night as City's nine-game winning streak came to an end.
Wing-backs Doherty - who signed a new contract on Friday - and Jonny stretched the City defence early on and the visitors' wide play eventually paid off. In the 25th minute, Doherty skipped by Chelsea loanee Jay Dasilva and squared for Cavaleiro to apply a simple finish.
Bristol City almost instantly replied when a deep cross found Callum O'Dowda inside the box in the 29th minute, but his overhead kick looped narrowly over the bar.
And on the half-hour mark, Doherty came agonisingly close to making it two, but his fierce shot after a fine one-two with Raul Jimenez rattled off the woodwork.
Lee Johnson introduced Pack and Taylor at half-time as the hosts switched formation, and the changes swung the momentum their way. Dasilva skied an effort, despite having time and space, over the bar in the 53rd minute after a spell of good City pressure.
In the 67th minute, Ruddy quickly reacted to a flicked shot by Taylor from point-blank range, seven minutes before Fielding was called into action to tip a 25-yard Joao Moutinho free-kick over the bar.
Second-half substitute Morgan Gibbs-White saw his one-on-one shot parried away by Fielding nine minutes from time, but City were ultimately made to rue two missed chances late on.
In the 87th minute, Pack sent his first-time shot from a corner over the bar as it flashed by him, before Fielding almost produced some emphatic late heroics deep into injury-time as he went up for a set-piece, but his half-volley was blocked by Ruddy.
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- Wolves have qualified for the FA Cup quarter-finals for the first time since the 2002-03 season, and the first time as a top-flight club since 1980-81.
- Bristol City have been eliminated from their last six FA Cup fifth-round ties (1981, 1990, 1992, 1994, 2001 and 2019).
- Matt Doherty has been involved in five goals in his last three FA Cup appearances (3 goals, 2 assists).
- Ivan Cavaleiro's goal for Wolves was the first shot of the match in the 28th minute.
- Since the start of the 2014-15 season, Matt Doherty has assisted more Wolves goals than any other player in all competitions (22).
- Bristol City suffered their first defeat in all competitions since losing 0-2 to Leeds United in November, ending a run of 15 games without defeat.
- Nuno Espirito Santo has won two away matches against Bristol City at Ashton Gate; only the second team he's won twice away from home at as Wolves boss, along with Sheffield Wednesday.
Man of the Match - Matt Doherty
Doherty was instrumental in helping Wolves get over the line against Bristol City and was a constant threat in the first half. His tireless running down the right flank was problematic to City's backline.
He was fully deserving of an assist after getting the better of Dasilva, and nearly got a goal of his own after combining well with Jimenez. He would have felt slightly aggrieved to have to come off in the second half with a minor injury.
What's next?
Bristol City travel to Norwich in the Sky Bet Championship on Saturday afternoon. Wolves visit Bournemouth in the Premier League at 3pm on Saturday.