As preposterous though it was that this tie rumbled into extra time, the Rangers support seemed to get added satisfaction from the belated nature of their team’s success. What a wonderfully fraught occasion this became. For the first time in 14 years, Rangers will compete in a European semi-final. That much seemed straightforward for 82 minutes of this Europa League quarter-final second leg, such was the dominance enjoyed by Giovanni van Bronckhorst’s side over a Braga team who had been reduced to 10 men before the interval. David Carmo’s late goal forced an added half hour and rumbles of concern in the stands. Rangers ultimately kept their cool and Braga, who finished the game with nine, lost their heads. The defining goal owed much to blissful simplicity. Fine interplay between Glen Kamara and Joe Aribo led the latter to cross for Kemar Roofe. The scale of celebration – epic, in fact – as Roofe slotted home was quite the sight. Despite the drama, Rangers are fully deserving of their last four place; they will not fear Leipzig given the elimination of Borussia Dortmund in an earlier round. With just five minutes played, it seemed strange to envisage what had been a subdued scene around Ibrox before kick-off. The unease, of course, could be attributed to domestic struggles that should see Celtic reclaim the Scottish title before long but Rangers have used recent seasons to deliver consistently strong European performances. Matheus, the Braga goalkeeper, will not count the opening goal anywhere near a collection of his finest moments. After a Borna Barisic cross from the left was flicked goalwards by Aribo, Matheus hesitated rather than beat James Tavernier to the ball. The Rangers captain stole in from full back to blast home from a tight angle. With the aggregate now level, Ibrox erupted. It did so again soon after, Roofe having headed another Barisic ball beyond Matheus from close range. The Braga players instantly and collectively swarmed around the referee, Francois Leteixer; the protests were deemed valid after Roofe’s goal was ruled out via VAR for a handball by Barisic. Roofe came within the underside of the crossbar of doubling the Rangers lead. The former Leeds man should really have scored. Braga’s approach was interesting in the sense that it allowed them to fire cross after cross into the penalty area. For the first half hour, this looked a bizarre tactic. The Portuguese looked panic-stricken each time Barisic or Tavernier tried to find Roofe from the flanks. Braga had offering nothing whatsoever in attack. Rangers were to claim the second goal their first-half dominance merited. Barisic chipped a pass from deep between the Braga defenders, allowing Roofe to capitalise. The forward was duly pushed over by Vitor Tormena, who was dismissed for what was a clear foul. Tavernier stepped forward after the dust had settled to stroke the penalty beyond Matheus. Rangers’ next task was to settle the tie, a scenario that looked imminent as they continued to exert control in the early stages of the second period. Aribo curled wide after starting and closing a sweeping move. If there was underlying Ibrox concern, it had foundation in the enforced absence of the prolific striker Alfredo Morelos. Minus him, it is always possible Rangers will suffer through bluntness. Connor Goldson attempted to offset any nerves, the centre-back’s snapshot flying wide off Matheus’s upright shortly after the hour. Aaron Ramsey, who did not enjoy a particularly convincing evening, headed over from Barisic’s cross and lashed a subsequent opportunity into side-netting. Roofe had his second goal of the evening chalked off, this time for offside after he lobbed the advancing Matheus. Tempers frayed in the immediate aftermath as the Braga substitute Vitinha was accused of catching Goldson in an aerial challenge. The officials shrugged off the incident. Van Bronckhorst had little cause to fear a late Braga hurrah. Carmo leapt unchallenged to nod past Allan McGregor from six yards and a corner. The Rangers goalkeeper had been a spectator for the previous 82 minutes. Braga’s small contingent leapt about giddy in the corner and no wonder; elation was matched by disbelief. Roofe’s key involvement was controversial given he had a lucky escape from a second yellow card beforehand. Instead, after he sent Rangers 3-1 ahead on the night it was Braga who had their numbers reduced further. Iuri Medeiros lunged into Leon Balogun before protesting vehemently in Leteixer’s face. Two yellow cards were swiftly issued. There ended Braga’s semi-final dreams. Rangers have Seville in their sights.