Wolves skipper Conor Coady said his team dug in to withstand Bristol City pressure and win through to the FA Cup quarter-finals.
Ivan Cavaleiro scored the only goal of the game at Ashton Gate as Premier League Wolves beat their Championship opponents 1-0.
City are in the Championship play-off places and put sustained pressure on the Wolves goal in the second half with both Jay Dasilva and Matty Taylor going close.
However, they couldn't force an equaliser and Wolves are in the last eight of the FA Cup for the first time since 2003.
Coady said afterwards that the team had shown the resilience necessary to beat determined opponents.
He told BT Sport: "It was a frantic second half, we knew it was going to be tough. I thought we dominated in the first half, but we stuck in there and showed we could defend.
"We knew we'd have defend. Sometimes you have got to dig in.
"We wanted to keep the same system as last year, we have a manager who's got an identity for this and we wanted to stick with that."
Wolves are seventh in the Premier League table in an impressive first season back in the top flight and only two of the sides above them will be in the quarter-finals of the FA Cup.
Manchester City have already booked their place, beating League Two Newport on Saturday while Monday night sees the final fifth round tie when Chelsea host Manchester United.
Wolves boss Nuno Espirito Santo said, on who he wanted in the quarter-finals, that he would just be happy to have a home tie at Molineux.
Wolves beat Liverpool in the third round of the competition, overcoming League One Shrewsbury after a replay in the fourth round.
Wolves are next in action on Saturday when they travel to the south coast to take on AFC Bournemouth. They are 8/5 for the win with Eddie Howe's side 17/10 and the draw 9/4.
Wolves are 12/1 to finish in the top six in the Premier League, they are 11 points behind sixth-placed Chelsea.
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