Kemar Roofe scored an extra-time winner as Rangers secured their place in the Europa League semi-finals with a 3-1 victory over nine-man Braga, who lost 3-2 on aggregate.
James Tavernier's first-half double, including a penalty awarded after Vitor Tormena was dismissed for a foul on Roofe, put Rangers in control with a 2-1 aggregate lead.
David Carmo's 83rd-minute header sent the tie into extra-time before Roofe, who had two goals disallowed, netted the decisive strike prior to Iuri Medeiros being given his marching orders.
Giovanni van Bronckhorst's men will next face RB Leipzig, who defeated Atalanta 3-1 on aggregate on Thursday, with the first leg of the last-four clash coming on April 28.
Rangers struck first when Tavernier rolled underneath Matheus at the back post after a deflection from Joe Aribo following Borna Barisic's cross.
The hosts were in dreamland three minutes later when Roofe headed home another delivery from Barisic, only for the goal to be ruled out for handball against the full-back.
Roofe then fired against the crossbar from point-blank range following Aribo's flick from a Tavernier corner as Rangers continued to dominate, and their reward arrived soon after.
Tormena was shown red for felling Roofe when through on goal, with Tavernier converting the penalty down the middle.
Roofe saw another strike ruled out in the second half, this time for offside, after chipping Matheus, before Carmo levelled with a powerful header from Medeiros' corner.
Conor Goldson nodded wide in the closing stages before extra-time, where Roofe latched onto Aribo's low cross to turn home from close range.
Medeiros was shown two yellow cards in quick succession for a foul on Leon Balogun and his subsequent riled reaction, before Scott Arfield hit the crossbar, but that miss did not come back to haunt Rangers.
What does it mean? Rangers overcome knockout specialists Braga
Braga had progressed from their previous nine ties in the UEFA Cup and Europa League when winning the first leg, with eight of those previous nine victories coming in home matches.
But Rangers ended that stellar record as they battled valiantly to overturn a first-leg deficit in Europe's secondary club competition for the third time in their last four attempts.
Now, Van Bronckhorst's men must overcome in-form Bundesliga side Leipzig to reach the final.
Terrific Tavernier
Tavernier offered Rangers the perfect start when he netted their fastest goal in the competition after just 71 seconds, and it was also the earliest Braga have conceded in the Europa League.
The hosts' captain then added his second from 12 yards as he became the joint-top scorer in this season's competition (six). No Rangers player has ever scored more in a single European campaign (also Alfredo Morelos in 2019-20 and James Forrest in 1964-65).
Vitor Tormen-ted
Tormena handed Rangers the perfect opportunity to take the aggregate lead by barging through the back of Roofe when he was one-on-one with Matheus.
Not only was the left-back given his early marching orders, but he also gave away possession the most times before his dismissal (eight) and was unsuccessful in all of his three duels.
Medeiros' red then made matters worse as Braga became the first side since Rangers last season to have two players sent off in the same knockout game in the competition.
What's next?
Rangers return to domestic action with an Old Firm clash against Celtic in the Scottish Cup semi-finals on Sunday, while Braga visit Estoril the following day.
Benzema: Mbappe must adapt to Madrid role and forget 'best in world' Vinicius
Kylian Mbappe must learn to play as a central striker at Real Madrid because he cannot displace Vinicius Junior on the left wing.
Those were the words of Los Blancos' second-highest scorer of all time, Karim Benzema.
Mbappe has scored eight goals in 14 appearances in all competitions for Madrid since his move from Paris Saint-Germain, but has failed to score in his last five games.
The 26-year-old has been deployed in a more central role since under Carlo Ancelotti, as opposed to the wide role where he enjoyed success with the Parisiens.
"The problem, in my opinion, is that [Mbappe] is not a central striker, even with the national team, every time he plays as a number nine he doesn't feel right, because that's not his position," Benzema said on Spanish television show El Chiringuito.
"On the left, he's got a guy who's at the same level as him, Vinicius, so there is a problem.
"You can't play Vinicius as a number nine or on the right, because when he plays on the left he makes the difference in every game.
"Mbappe isn't a real number nine. People ask a lot of him and he's under a lot of pressure, this isn't Paris Saint-Germain."
The France captain has underperformed his expected goals (xG) figure in LaLiga by 1.75 this term, recording a shot conversion rate of just 18.18% from his 33 total attempts.
He has also missed seven big chances, with only Real Betis duo Abde Ezzalzouli and Vitor Roque (both eight) and Barcelona's Robert Lewandowski (11) wasting more in LaLiga.
In Madrid's last game, a 4-0 Clasico defeat, Mbappe recorded just 27 touches. Only Aurelien Tchouameni (24) registered fewer among those who started the encounter.
Benzema also endured a difficult start to life in the Spanish capital, netting just nine goals in his 33 appearances in all competitions in his debut season after his move from Lyon.
He would, however, go on to become one of Madrid's best ever players, scoring 354 times in 648 outings, a total that puts him behind only Cristiano Ronaldo (450) in the club's history.
Benzema won 25 major honours during his time at the club, also scooping the Ballon d'Or in 2022, and had some advice for his compatriot moving forward.
"Don't give up, because I don't think he's going to push Vinicius to move. He's the best player in the world at the moment," Benzema added.
"Mbappe needs to get it into his head that today he's a number nine, and forget about the left flank for a while."
Mbappe will be back in action for Madrid on Tuesday when they face Milan in the Champions League.
Luis Enrique in awe of Simeone energy ahead of reunion
Paris Saint-Germain coach Luis Enrique was full of praise for his former rival Diego Simeone as he prepares to go head-to-head with the Atletico Madrid boss in the Champions League.
PSG and Atletico, who reached the semi-finals and the quarter-finals respectively last season, will face off on Wednesday having both won just one of their three league-phase games.
A home victory would boost PSG, currently 19th with four points, while Atletico, languishing in 27th on three, are aiming to recover from back-to-back losses.
PSG have never faced Atletico in the Champions League before but Luis Enrique's Barcelona defeated Simeone's Atletico side nine times in their 14 meetings between 2014 and 2017, drawing twice and losing three times.
Luis Enrique led Barca to a Champions League and LaLiga double in 2014-15 followed by another league title the following year.
"We've played against each other as players and then as managers. I admire Simeone, when a coach can stay for so many years at a top club it means he is great because that is such a difficult thing to do," Luis Enrique told reporters on Tuesday.
Simeone has managed Atletico for 13 years, guiding them to two LaLiga titles and two Europa League crowns, though the Madrid side had considered hiring Luis Enrique prior to Simeone's arrival.
"I had given my word to another club. If I had gone to Atleti, I would not have stayed half as long as Simeone because I don't have the energy as him," added Luis Enrique.
"They are lucky to have found Simeone as a coach. You need a lot of energy, to be able to convince all your players over the long-term."
PSG, having lost Kylian Mbappe to Real Madrid in the close season, have just two goals in their three Champions League games, beating Girona 1-0 but drawing 1-1 with PSV and losing 2-0 at Arsenal.
"I have no doubt we can improve in defence and attack, whether it is with the defender duos of Marquinhos and Willian Pacho, or Milan Skriniar and Lucas Beraldo, or in the midfield," Luis Enrique said.
"I understand you want to discuss individual players, but we analyse things from a broader perspective.
"What interests me is to always generate goalscoring opportunities and to arrive in the penalty area because you have managed to be stronger than your opponent.
"That is my objective as a coach: to always generate opportunities."
Close-season signing Matvey Safonov, who kept a clean sheet in their opening win against Girona, might replace number one goalkeeper Gianluigi Donnarumma, whose mistakes proved costly at Arsenal and against PSV.
"You will find out tomorrow. After a good cup of cappuccino, I will decide who the goalkeeper is," Luis Enrique said.
Neymar suffers fresh injury blow
Neymar sustained a new injury as he was forced off during Al-Hilal's AFC Champions League Elite win over Esteghlal.
Aleksandar Mitrovic plundered a hat-trick on Monday to seal a 3-0 win.
But Al-Hilal's victory was soured by an injury to Neymar, who had to make way just 29 minutes after he came on as a second-half substitute.
The Brazilian, who has just returned from over a year out of action following a serious knee injury, was forced off with what appeared to be a thigh issue.
Indeed, Monday's appearance was only the 32-year-old's second for Al-Hilal since his comeback.
He has featured just seven times for the Saudi Pro League champions in all competitions since his big-money move from Paris Saint-Germain in 2023.
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