A second-minute strike from midfielder Mario Lemina handed the Black Country side an ideal start to proceedings in the fifth-round tie, and they were ultimately able to hold out and seal their progression into the last eight.
The Seagulls piled the pressure on in the second period and had chances to level the scores late on - most notably via goalkeeper Jason Steele - however the visitors were forced to say farewell to their FA Cup dreams in the West Midlands.
After a narrow success over Roberto De Zerbi's men, Wolves have been handed a home quarter-final clash with Championship side Coventry side - the lowest-ranked club left in this year's competition.
With a Premier League jaunt up to Newcastle United on Saturday afternoon at the forefront of Gary O'Neil's thinking, Wolves made four alterations from the side which defeated Sheffield United on Sunday, with Santiago Bueno, Matt Doherty, Jean-Ricner Bellegarde and Tommy Doyle entering the XI.
Hit by a number of key injuries and fitness issues in their striking department, including the likes of Evan Ferguson and Danny Welbeck - who took up a place on the bench - Barcelona loanee Ansu Fati made a rare start for De Zebri's team, whilst Australian Cameron Peupion made his full debut for the club.
Wasting no time in staking his claim for a spot in the Premier League starting XI, Bellegarde's industrious run from the attentions of Jan Paul van Hecke allowed the Haiti international to send in a admittedly-tame cross towards Steele in the visitors' net after just two minutes.
The Seagulls' second-choice goalkeeper was disorientated under the flight of the ball and parried into the path of the onrushing Lemina, who produced a sliding effort to beat the 33-year-old stopper and hand Wolves a massive advantage in the early stages of the last-16 clash.
Despite taking the lead early on, the Black Country outfit failed to create much for the remainder of the first half, although Brighton were offering their hosts a glimmer of goalscoring action courtesy of some risky passing out from the back, with keeper Steele clearly unnerved in the aftermath of his second-minute blunder.
Evading the attentions of Doherty on the left-hand side, Pervis Estupinan gifted Facundo Buonanotte an exceptional chance to level the scores in the 38th minute after the Ecuadorian delivered a sweet delivery onto the head of the Argentine, however he was unable to keep his effort on target.
Following a timid shot which failed to worry the unstung palms of Jose Sa in the closing moments of the first period, 21-year-old Peupion was replaced at the half-time break by former England international Welbeck, with De Zebri seeking to solve his side's attacking deficiencies from the opening 45.
With his last-gasp equaliser against Everton on the weekend fresh in the mind, Lewis Dunk had a decent opportunity to find the net after a corner-kick delivery, however the Brighton captain was stumbling back as he attempted to make contact, ultimately firing wide of Sa's net.
The Seagulls' half-time alteration was swinging the game's momentum before a stoppage in play, when Wolves' leading marksman Hwang Hee-chan went down in some distress after playing a forward ball, and it was clear to see that the South Korean international had suffered a hamstring strain.
O'Neil's side perked up in the contest following the arrivals off the bench of regular starters Pedro Neto and Pablo Sarabia, with the former's blistering run leaving Dunk on the floor before Igor Tudor was able to slow the Portuguese winger down when he threatened to strike and double the hosts' advantage.
As time to grab an equaliser evaporated, Brighton increasingly turned to a more direct approach against a side without the towering Craig Dawson in their backline, although multiple scrambles inside the Wolves box rarely resulted in meaningful chances for the visiting Seagulls.
The final 10 minutes of the clash saw De Zerbi hand an English-football debut to highly-rated Argentine Valentin Barco, who joined the South Coast club from South American giants Boca Juniors in January, however the 19-year-old was unable to inspire his side to a late comeback in the West Midlands.
Brighton did not exit the competition out of a lack of trying, though, with the Seagulls having a good opportunity in added-on time to force the contest into extra time, however the golden chance from a corner fell to the unmarked feet of keeper Steele, who made little contact with his strike which dribbled past the wrong side of the post.
After booking their spot in the quarter-finals of the FA Cup for only the third time this century, Wolves will continue their pursuit of European football in the Premier League when they travel to Eddie Howe's Newcastle on Saturday.
The Seagulls still have a chance of lifting a first-ever major honour in the form of the Europa League this season, but before an eye-catching clash with Italian giants Roma on the continental stage, De Zerbi's charges will resume their league schedule at Fulham on the weekend.