Morgan Gibbs-White came up with an injury-time winner for Wolves after Brighton's Lewis Dunk scored and was then sent off in a 2-1 victory for the hosts at Molineux on Sunday.
At half-time the Seagulls had looked on course for a win which would have taken them to 40 points and made them mathematically safe from relegation, thanks to Dunk's towering header on 13 minutes.
However, Brighton were left to play the final 37 minutes with 10 men after Dunk grabbed Fabio Silva's shirt as he ran through on goal, and substitute Adama Traore fired Wolves level (76).
Gibbs-White had passed up a great chance to score his side's second when he blasted over from 16 yards with the goal at his mercy but he made no mistake from a similar position with 90 minutes on the clock, earning Wolves a first-ever win over Brighton in the top flight.
Brighton's situation got even worse at full-time when Neal Maupay was also shown a straight red for arguing with referee Jon Moss but they still have a 10-point cushion on third-bottom Fulham.
If the Cottagers lose to Burnley on Monday Graham Potter's side will be assured of another season in the Premier League - but they will be kicking themselves for not doing it under their own steam at Wolves.
Wolves: Patricio (6), Hoever, (6), Coady (6), Kilman (7), Ait-Nouri (7), Neves (6), Moutinho (7), Gibbs-White (8), Vitinha (7), Podence (6), Silva (7).
Subs: Traore (8), Jose (5), Dendoncker (N/A)
Brighton: Sanchez (6), White (6), Webster (6), Dunk (5), Burn (7), Gross (7), Bissouma (6), Trossard (6), Jahanbakhsh (6), Maupay (6), Welbeck (7).
Subs: Mac Allister (6), Zeqiri (N/A), Moder (6)
Man of the match: Morgan Gibbs-White (Wolves)
How Wolves turned it around...
With the hosts set for a mid-table finish, Nuno made five changes and fielded the youngest Wolves starting XI for a Premier League match in almost 12 years, but they started brightly, with Vitinha forcing Robert Sanchez to tip his shot around the corner early on.
However, the game changed on 13 minutes when Brighton scored with their first effort at goal, as Dunk towered above the Wolves defence to meet Pascal Gross' corner and power his fifth Premier League strike of the season into the bottom corner.
Set-pieces proved to be a real problem for Wolves during that first half, with Dan Burn furious he wasn't awarded a penalty when he was held back by Gibbs-White, before Dunk headed at goal from consecutive corners, out-jumping the mis-matched Ruben Neves.
Maupay came close to adding a second on 28 minutes, hooking a Danny Welbeck knock-down over the bar with his left-foot, but Wolves managed to not fall any further behind by the break.
Wolves made five changes from their 1-1 draw with West Brom, with Daniel Podence, Ki-Jana Hoever, Morgan Gibbs-White, Joao Moutinho, and Max Kilman coming in. Adama Traore, Owen Otasowie, Romain Saiss, Leander Dendoncker, and Nelson Semedo missed out.
As for Brighton, they made one change from their 2-0 win over Leeds, with Alireza Jahanbakhsh replacing Joel Veltman.
Nuno used the interval well and Wolves came out with far more purpose in the second half - and they were handed a huge boost on 53 minutes when Vitinha nipped a pass through the Brighton defence for Fabio Silva to run onto and the slow-turning Dunk hauled down the striker.
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The Brighton man could have few complaints about the straight red card and waves of Wolves attacks followed his exit, with Gibbs-White testing Sanchez twice from the edge of the box, before substitute Willian Jose just failed to latch onto Joao Moutinho's cute chipped through ball.
It was another Wolves replacement who eventually pulled the hosts level with 15 minutes to play, Traore - who had been involved in an intriguing battle on the right flank with Burn - came inside and, after exchanging passes with Silva in a crowded penalty area, blasted home the equaliser.
Wolves should have scored a second on 84 minutes when Traore broke past Sanchez after running onto a long ball, and pulled the ball back for Gibbs-White but the 21-year-old sent a woeful effort over the unguarded goal.
There was time for a reprieve for the young Wolves forward, though, with Gibbs-White netting his first Premier League goal on the stroke of 90 minutes by firing into the top corner to win it for his side.
Brighton's frustration of throwing away the points told at full-time, as Maupay was shown a straight red for remonstrating with ref Moss.
What the managers said...
Wolves boss Nuno Espirito Santo: "We got a little bit of luck in the final moments of the game but we chased that moment a lot. The message in the first half was trying to correct, to find better solutions, but the main message was energy. We didn't have energy in the first half. I was really disappointed with the first half but I was happy we changed that.
"It seemed in the previous game at home we seemed flat, too. It's something we're worried about. I'm sure one of the things is a lack of fans and I'm sure when they return it is going to be better than ever."
Brighton boss Graham Potter: "First half we were good, deservedly in the lead and looking to add to that. We started the second half slowly and sloppily and the result is then the red card happens and when it happens so early it's difficult to keep them out.
"It's frustration from Neal [Maupay for second red card] and he needs to handle that better. We're disappointed with the result, until you're mathematically there you have to keep fighting and that's what we have to do."
Opta stats - Wolves finally land a top-flight win over Brighton
- In what was their 12th such meeting, Brighton lost to Wolves in the top-flight for the very first time, having won seven and drawn four of their first 11 top tier league clashes.
- Since Wolves returned to the Premier League in 2018, only Manchester United (54) have recovered more points from losing positions in the competition than Nuno Espírito Santo's side (51).
- No side has dropped more points from winning positions in this season's Premier League than Brighton (23, level with Southampton).
- Since they returned to the Premier League in 2018, only Liverpool (7) have scored more winning goals in the 90th-minute or later of matches in the competition than Wolves (6).
- No team has been given more Premier League red cards this season than Brighton (five, level with Arsenal), with Lewis Dunk the first player to be dismissed twice in the 2020-21 competition.
Wolves go to Tottenham next Sunday, live on Sky Sports at 2.05pm, while Brighton host West Ham live on Sky Sports on Saturday at 8pm.