Midfielder Ivan Cavaleiro's first-half finish brought City's 15-match undefeated run and nine-match winning streak to a halt.
The Championship club had their moments, but ultimately could have few complaints after they struggled to consistently impose themselves on the fifth-round contest.
Wolves had not reached the competition's last eight since 2003, but Nuno Espirito Santo's team look solid bets to maybe go all the way to Wembley this season.
City boss Lee Johnson made five changes from the side which beat QPR in the Championship on Tuesday, including starts for Joe Morrell, Kasey Palmer and Niclas Eliasson.
Wolves, meanwhile, showed three switches following a 1-1 draw against Newcastle last time out, with Cavaleiro, goalkeeper John Ruddy and Romain Saiss all called up.
And the visitors made a bright start, with plenty of possession finding its way on the right to Matt Doherty, who twice put in early crosses that tested City defensively.
Even though clear-cut chances were at a minimum, Wolves continued to dominate territory and possession, with City's most lively threat coming through Palmer's impressive movement.
But they could not shackle Doherty, and it was no surprise that he created an opening goal for his team after 28 minutes.
He found space just outside the box, easily cut inside Jay Dasilva and crossed, before Cavaleiro side-footed past a prone home goalkeeper Frank Fielding.
It was a deserved reward for Wolves' dominance, and Doherty almost came up trumps again two minutes later when he fired an angled shot past Fielding that glanced off the post.
Wolves had a grip on the contest, and with City struggling to stem the tide of opposition ball in midfield, they needed a diving save from Fielding to deny Leander Dendoncker.
Johnson's men just could not handle Doherty, and another superb pass found Raul Jimenez in space, but he fell to the ground and the half-hearted penalty claims were waved away by referee Martin Atkinson.
City had made little impression during the opening 45 minutes and there was a muted feel around the stadium as Wolves closed out the half by remaining in control.
Johnson made a double change at half-time, sending on Matty Taylor and Marlon Pack, and Taylor's presence quickly offered far more of a threat before his captain Bailey Wright was booked for a clumsy challenge on Cavaleiro.
Ruddy was then forced to make a sharp save down to his left as City pressed for an equaliser, and they looked a team transformed from their ineffective first-half effort.
Wolves, though, remained dangerous, and Fielding tipped a 75th-minute free-kick from Joao Moutinho over the bar.
But back came City, building sustained pressure on Wolves' defence. Callum O'Dowda shot straight at Ruddy, and then the visiting goalkeeper turned another effort wide for a corner.
It was to prove City's last notable assault on Ruddy's goal, and Wolves closed things out to join the likes of Manchester City, Watford and Millwall in the quarter-finals.