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.
Al Hilal 3-1 Al Fateh: Neves on target as Saudi giants close in on title
Al Hilal moved 12 points clear of Cristiano Ronaldo's Al Nassr at the top of the Saudi Pro League as Ruben Neves scored in a 3-1 win over Al Fateh on Friday.
Former Wolves star Neves slotted in from the penalty spot in the 74th minute, as Al Hilal completed a rapid comeback.
Having fallen behind to Lucas Zelarayan's 57th-minute opener, Al Hilal responded swiftly through Micheal before Salem Al Najdi fouled Mohammed Al Qahtani in the penalty area.
Ex-Barcelona winger Cristian Trello and Al Fateh coach Slaven Bilic were booked for their complaints, with Neves making no mistake, paving the way for Ali Al Bulayhi to seal victory in the 15th minute of an extended period of stoppage time.
Data Debrief
Al Hilal have now won 21 games on the spin in the league. They have scored 86 goals across their 28 matches this season, winning 26 in total.
They had 19 shots on Friday, accumulating 2.34 xG to Al Fateh's 0.25, with pass-master Neves creating three chances to go along with his goal.
RFEF elects Rocha as new president
The Spanish Football Federation (RFEF) has confirmed Pedro Rocha as its new president.
Rocha has been elected as Luis Rubiales' replacement, despite being under investigation for corruption.
He had been serving as interim president since Rubiales resigned in September over the scandal caused when he kissed player Jenni Hermoso following Spain's Women's World Cup triumph in August.
In a statement released on Friday, the RFEF said: "Pedro Rocha has today been proclaimed the new president of the Royal Spanish Football Federation (RFEF), after having received the support of the majority of the assembly members of this institution that governs Spanish football.
"The process followed the procedure agreed by the Electoral Commission, which met this morning, and the timetable that was established for these elections."
Rocha has been under investigation since earlier in April, after the RFEF's headquarters was raided by police last month. The Spanish government announced on Thursday that it would be stepping in to oversee the running of the organisation.
Guardiola insists three teams still in title hunt despite Liverpool slip-up
Pep Guardiola insists Liverpool remain in the Premier League title race, despite the Reds losing further ground on Arsenal and Manchester City in a dramatic few days at the summit.
Liverpool suffered a surprise 2-0 defeat to Merseyside rivals Everton on Wednesday, a result which meant they failed to close the gap to Arsenal after the Gunners thrashed Chelsea 5-0 on Tuesday.
While Jurgen Klopp's men couldn't respond to the Gunners pulling clear, City did on Thursday, with Phil Foden scoring twice in an emphatic 4-0 win over Brighton at the Amex Stadium.
One point behind Arsenal with a game in hand, City know five wins from their five remaining matches will seal an unprecedented fourth successive English top-flight title.
However, Guardiola expects further twists and turns in the coming weeks.
Asked if Liverpool were still in contention after City's win, Guardiola told Sky Sports: "Yeah. Many things can happen.
"What happened with Liverpool, losing to Crystal Palace and Everton, can happen to us. It can happen to Arsenal. No-one is safe. We have to rest. Now it is just about recovering for the next one.
"We have been here in the past but being here in the past doesn't mean it is going to happen. We have to do the things to make it happen."
City's comprehensive win – in which Kevin De Bruyne scored his first headed goal in the Premier League – saw them cut Arsenal's goal difference advantage to eight goals.
However, Guardiola believes it will be tough for City to close that gap, saying: "It is difficult to cut. The margin is so big. They score a lot of goals and don't concede.
"The main thing is to win the games. We have five games left and they are tough ones – it's a lot of games. We'll take it one game at a time."
Foden's first goal against Brighton – a deflected free-kick – saw him become just the third player to score 50 top-flight goals under Guardiola while aged 23 or younger, after Erling Haaland and Lionel Messi.
Foden is the favourite to be named Premier League Player of the Season, and while Guardiola believes he should be in contention, he says his player is more concerned with team honours.
"For sure, but he wants to win the Premier League," Guardiola said when asked if Foden deserved individual honours. "His influence in the final third was better than in the last two or three games. Today he was more calm, his decision-making was good and to score goals is always good."
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