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.

Rangers boss Giovanni van Bronckhorst saluted his players as they sent Borussia Dortmund crashing out of the Europa League, describing the 6-4 aggregate victory as "a big moment for the club."

Leading 4-2 after a stunning first-leg performance at Signal Iduna Park, the reigning Scottish Premiership champions endured a tense second leg at Ibrox.

Despite James Tavernier's first-half penalty, Jude Bellingham and Donyell Malen reduced the aggregate deficit to a single goal before the break.

Indeed, Malen might have dragged Dortmund level in the tie, but Tavernier drilled in his second just before the hour mark, ultimately booking the hosts' place in the last-16 draw despite Rangers having a third disallowed after a VAR check.

"It is a big moment for the club, we can make a lot of people proud as it was a difficult game again," Van Bronckhorst told BT Sport.

"We were very unfortunate in some moments where we could have cleared the ball. We had to change something to be more defensively solid.

"[Alfredo] Morelos was much stronger in the second half, and we had many more dangerous moments.

"We trained with three different plans for today. We needed to have scenarios in place to be executed, and I'm glad we did.

"We had a great performance; we played them twice and got four points – it’s a great performance. 

"The last 16 is only top teams; we wait for them, and we look forward to the draw."

Dortmund star Bellingham suggested he and his team-mates only had themselves to blame.

"It was brilliant to play in. A good team, a good test," the England international told BT Sport, having created a joint team-high three chances.

"We didn't have the bite we had in the first half. It's just one of those nights, we didn't take all our chances and they took theirs, fair play to them.

"We've let the fans, the staff and ourselves down. If we look at ourselves in the mirror, we'll realise we could've done more."

Bellingham is not wrong. Dortmund finished with a higher expected goals (xG) than Rangers (2.97 to 2.26).

Two-goal Tavernier, meanwhile, revealed that a tactical reshuffle at the break proved instrumental for Rangers.

"We really stepped up in the second half after we changed tactically, it allowed us to progress," Rangers' captain explained.

"The manager told us that we have to follow the runners and tighten it up a bit; that’s what we do in our back five system, and it works for us.

"We are really impressive, the result was pleasing. I always try to get to back post, and I got the goal today.

"This game shows the character that we have in the squad; we have a great squad that can push through."

Rangers have qualified for the round of 16 in the Europa League for a third consecutive season, which is their longest streak of reaching at least this stage in a major European competition since a run of three between 2005-06 and 2007-08 – they reached the final of the UEFA Cup in the last season of that previous run.

Dortmund, meanwhile, have been eliminated in three of their past four two-legged ties in the knockout stages of the Europa League, losing against Liverpool in the 2015-16 quarter-finals, Salzburg in the 2017-18 round of 16 and Rangers this season.

James Tavernier scored twice as Rangers booked their place in the Europa League last 16 with a 2-2 draw against Borussia Dortmund, which sealed a 6-4 aggregate win.

A week on from their brilliant 4-2 triumph at Signal Iduna Park, Rangers had their captain to thank as they secured progression on a frantic night in Glasgow.

Tavernier opened the scoring from the spot in the 22nd minute, but the excellent Jude Bellingham equalised for Dortmund before Donyell Malen put the visitors ahead.

Rangers' resolve returned in the second half, though, with Tavernier drilling in his second just before the hour to end BVB's Europa League hopes.

Bellingham had hit the post as Dortmund looked to deflate the raucous atmosphere at Ibrox, but having withstood the early pressure Rangers went ahead – Tavernier slamming a penalty down the middle after Julian Brandt fouled Ryan Kent.

Brandt wasted a chance to make immediate amends, but Bellingham restored parity when he slotted in after pouncing onto Connor Goldson's poor touch.

Scott Arfield and Alberto Morelos went close for Rangers before Allan McGregor brilliantly denied Malen at the other end in the space of a minute.

McGregor had no chance when Malen prodded past him in the 42nd minute to put Dortmund ahead, however.

Gregor Kobel got down to Morelos' goal-bound shot after the restart, but BVB were made to pay for more dismal defending when Tavernier lashed in at the back post from Joe Aribo's cross.

Dortmund seemed set to regain their lead when Marco Reus rounded McGregor but sliced into the side-netting.

Instead, Rangers were in delirium when Morelos raced through and squared for Kent to tuck in, only for referee Antonio Mateu Lahoz to harshly disallow the goal for a foul on Emre Can after a VAR check, although it ultimately mattered not.