Rock-solid in this stadium carved into an old quarry, Rangers marched into the Europa League last-16 with a margin of victory that flattered only their previously imperious hosts.
This was close to a textbook away performance by Steven Gerrard's side. In stark contrast to their woes on the road domestically, here they were a perfect picture of tactical discipline and counter-attacking punch against the competition's top scorers.
No team had blanked out Braga in any of their 11 previous Europa League matches.
The game-plan formulated by Gerrard delivered an outstanding result that might stand as his best in an impressive 30-outing European record.
Not since season 2010-11 have the Ibrox club advanced this far in continental competition. They can now look forward to Friday's draw and the exciting possibilities it might bring.
Ryan Kent's exquisitely-taken second-half winner made sure of progression in northern Portugal and was the very least Rangers deserved.
By that point, they had seen an Ianis Hagi penalty saved and a couple of prime chances slip away. The fear at half-time was of profligacy being punished, but a redoubled effort ensured that fantastic first-leg comeback was built upon in the best possible way.
There were times when they had to defend doggedly. But a back four that included George Edmundson ahead of the dropped Niko Katic rose to the task superbly.
Again, the difference from Sunday's 2-2 draw with St Johnstone was extraordinary.
Gerrard will hope the confidence boost can carry into Saturday evening's Scottish Cup quarter-final against Hearts as they pursue what looks increasingly like their last chance of silverware in Scotland. Following up on this success would breathe new life into a previously flagging season.
Gerrard's call to ditch Katic was huge, albeit not entirely unexpected. The Croat's confidence looked shredded as he produced an error-strewn performance in Perth.
While praising Katic's attitude at Tuesday's press conference, Gerrard had been coy about the likelihood of him continuing alongside Connor Goldson. The decision instead was to give Edmundson a first European appearance since a 2-0 win over Progres Niederkorn way back in July.
What a night this was for the young Englishman. Nerves were to be expected. They doubtless doubled when he gave the ball away to Fransergio with his very first involvement.
Mercifully, the Brazilian midfielder couldn't pick a sufficiently precise through-ball to expose the error.
Braga's groundstaff had gone heavy with the sprinklers just prior to the teams emerging, making the surface somewhat slippy. Edmundson was one of several Rangers players to lose their footing early doors. Finding composure wasn't instant. But when it arrived it should have led to a ninth minute lead.
A slick one-two between Scott Arfield and Kent enabled the former to burst behind Braga's persistently high defensive line. Arfield should have perhaps taken the shot himself as he homed in on the 18-yard box, but opted to dab it left to the supporting Kamberi. His low drive from an angle was thwarted by home keeper Matheus.
Incredibly, an even better chance was spurned ten minutes later. Gerrard could hardly have wished for two better sights of goal with less than a quarter of the game played. To see neither taken must have made his heart sink.
The creation of this one was all about Hagi. Hero of the first leg, the Romanian forced a mistake from Raul Silva before skipping past David Carmo to surge into the penalty area. He pulled the ball back for Kent but the winger failed to hit the target from 12 yards, tugging his shot wide of Matheus' right-hand post.
Braga had issued an appeal for businesses to let workers leave early and make the 5pm kick-off. Those who answered the call were being given heart flutters by their team's defending. They had to to wait until the 26th minute for real excitement at the opposite end.
A fine, pacy cross from left wing-back Nuno Sequeira picked out Paulinho for a header tipped over the bar by Allan McGregor. Yet again, the veteran was proving his worth on the continental stage.
That was as scary as it got for the Ibrox outfit prior to the break. Adherence to Gerrard's instructions was giving control and security. All that was missing was a goal.
Right on half-time, a penalty provided the perfect window to address that and banish the memory of those earlier misses. But Rangers have been cursed from the spot this season.
Raul Silva handled as he sought to clear a Kent corner, with Swedish referee Andreas Ekberg confirming the award after a VAR check.
Hagi stepped up but Matheus guessed the right way and thrust up a strong hand to repel. It was a fine save, but also the sixth penalty out of 10 Gerrard's side have missed this term. Hagi is the fourth different taker to fail.
The tie could – should – have been done and dusted by the break. Instead, the tension lingered into the second period. Braga coach Ruben Amorim moved first with a change, replacing Joao Palhinha with Joao Novais in central midfield. The unconvincing Raul Silva succumbed to injury not long after to bring Galeno into the fray.
Still the chances came Rangers' way. Ten minutes after the restart, Kamberi and Steven Davis swapped passes to give the striker space to cross towards the near post. This one was at an awkward height for Kent as volleyed over the top.
He would soon have his moment. With 61 minutes on the clock, Kent delivered the long-awaited incision in terrific style.
Hagi's sweeping ball over the top sent him scampering through the inside left channel. There was still plenty to do even after he evaded Sequeira's attempt at a covering challenge, but the former Liverpool player did it with aplomb. As Matheus advanced, Kent produced a brilliant angled finish that bounced inside the far post.
A response was always going to have to be weathered. Rangers did it admirably, even if there was a slice of good fortune when Horta's downward header from a Trincao cross clipped the outside of McGregor's left-hand post.
The outstanding Arfield was then flagged offside when tapping in after a Goldson header hit an upright before, in stoppage time, substitute Sheyi Ojo saw a long range drive tipped wide by Matheus.
Rangers merited a second goal. This, however, was not a night for complaints. Just immense satisfaction about a job expertly done.