Coming back from behind, Gibbs-White grabbed his first Premier League goal after Lewis Dunk's costly red card for the Seagulls.
Dunk earlier put Graham Potter's outfit in front as he took advantage of shoddy marking from a corner.
Nuno Espirito Santo's side, though, were handed the initiative as the defender tugged down Fabio Silva – and they took advantage.
Superb substitute Adama Traore levelled things up before Gibbs-White, having spurned a glorious chance a couple of minutes beforehand, came up with the winner.
Brighton attacker Neal Maupay was sent off after the final whistle for voicing his displeasure towards referee Jonathan Moss.
Now, Wolves have trips to both Tottenham and Everton before ending the campaign – with fans finally returning – at home against Manchester United.
It was a moment of elation and relief in equal measure as Gibbs-White opened his top-flight account to seal all three points.
His miss from close range after being set up by the brilliant Traore was unfathomable, but it does not matter after he showed persistence and precision to net in the 90th minute. Well done.
Wolves, on the whole, deserve credit for making the man advantage count as well.
They had been torrid in the first period after allowing Dunk to head home but they stepped up the intensity after the break – and the youngsters, like they did against Albion, played their part.
Traore, though, made the difference off the bench.
The tiring Seagulls simply could not do cope with his relentless running. He took his goal with aplomb and kept plugging away.
This performance was not without its flaws, of course. Wolves' defending from set pieces continues to be downright bad. They are just not tracking runners.
But come the end, they had shown grit and character.
It is not all sunshine and rainbows, but supporters can take heart from that as a limited amount of them prepare to finally be back inside in their beloved ground.
Nuno saw this game as an opportunity to experiment and duly rang the changes.
There were five in total from the Black Country derby draw at The Hawthorns, with Ki-Jana Hoever, Max Kilman, Joao Moutinho, Daniel Podence and Gibbs-White coming in.
Nelson Semedo, Romain Saiss, Leander Dendoncker and Traore dropped to the bench while Owen Otasowie did not make the squad because of a knock.
Brighton, meanwhile, made just one change from their 2-0 victory over Leeds as Alireza Jahanbakhsh replaced Joel Veltman.
Hoever, Kilman and Gibbs-White were making their first Wolves starts since March, February and January respectively – and they looked fairly sharp early on.
Nuno's side were spraying the ball around quickly and confidently.
Rayan Ait-Nouri, having stepped up his game in recent months, surged forward and played a clever one-two with Podence before feeding Vitinha, whose shot was tipped wide by Robert Sanchez.
Wolves dominated possession for the opening 10 minutes and for the first time in a good while, they were playing attractive football.
But old habits die hard and, yet again, they were undone from a set piece. Things predictably unravelled from there.
Dunk comfortably beat Ruben Neves to the punch, heading an outswinging corner beyond the helpless Rui Patricio in the 13th minute.
Nuno's lot have failed to deal with corners and free-kicks all season, and they even continued to make the same mistakes after the goal.
Gibbs-White was seen trying to mark the 6ft 7in Dan Burn, who, thankfully, nodded the ball straight into Patricio's hands. Scorer Dunk was then unchallenged from the next corner, with Patricio having to pull off a magnificent save to deny him.
Wolves are not blessed with a great amount of height, but surely there is a better way of setting up?
Brighton squandered another decent opportunity to double their lead as Danny Welbeck's knock-down was volleyed over by strike partner Maupay, and the hosts ended the half offering nothing.
The attacking threat had completely disappeared, with lone centre forward Silva not having a touch. An all too familiar tale.
Wolves, though, were still in the game and had a couple of efforts at the beginning of the second period.
Centre-half Kilman decided to try his luck from range and saw his low fizzer, eventually, gathered by Sanchez. Gibbs-White also clipped the post having worked himself a yard of space.
And then, pretty much out of nowhere, came Dunk's dismissal.
Pulling Silva down as the last man after he was released by Vitinha's deft through-ball, it was an obvious red and gave Nuno's men a huge opportunity to turn it around.
Not long after the sending off, Traore entered the fray for the sluggish Neves. Willian Jose replaced the also-ineffective Podence, and Wolves got their leveller.
The fleet-footed Traore broke into the area, played a neat one-two with Silva and lashed the ball beyond Sanchez before he knew anything about it.
It was a well-worked goal and Wolves wanted another one, with Dendoncker coming on for Vitinha. A golden opportunity soon arrived, too.
Traore – being the impact substitute Nuno hoped he would be – dispossessed keeper Sanchez and squared it to Gibbs-White.
All he had to do was find the target from around 10 yards out, but he ballooned his strike into the South Bank.
It appeared Wolves would come to rue that miss but Gibbs-White made amends.
He emphatically curled the ball into the top corner and left the pitch with an enormous smile on his face. Brighton, meanwhile, also had Maupay sent off for dissent after the final whistle. A topsy-turvy, very eventful afternoon.
Wolves (4-2-3-1): Patricio; Hoever, Coady (c), Kilman, Ait-Nouri; Neves (Traore, 61), Moutinho; Gibbs-White, Vitinha (Dendoncker, 77), Podence (Jose, 69); Silva
Subs: Ruddy (gk), Semedo, Saiss, Richards, Cundle, Corbeanu
Goals: Traore (76), Gibbs-White (90)
Brighton (4-4-2): Sanchez; White, Dunk (c), Webster, Burn; Jahanbakhsh (Moder, 58), Bissouma, Gross; Trossard (Mac Allister, 58); Maupay, Welbeck (Zeqiri, 78)
Subs: Steele (gk), Tau, Alzate, Propper, Izquierdo, Connolly
Goal: Dunk (13)
Red Card: Dunk (53)
Referee: Jonathan Moss (Sunderland)