Rangers last reached the last 16 of European competition in 2011, when they qualified from the Champions League group stage
Rangers backed up last week's stunning comeback by producing a poised performance to dump Braga out of the Europa League and reach the last 16.
Ryan Kent's calm, breakaway finish coupled with a strong defensive display means the Ibrox side are in the last 16 in European competition for the first time since 2011.
It might have been more comfortable had Ianis Hagi not had a first-half penalty saved and Scott Arfield's late attempt from close range not been correctly ruled out for offside.
But few would have given Steven Gerrard's side a hope of progressing against the Europa League's top scorers, having been 2-0 down after an hour of the home leg.
Kent's strike, though, ensured a 4-2 aggregate victory and means Rangers can look forward with excitement to Friday's draw at 12:00 GMT in Nyon.
- Reaction & as it happened
Master counter-attackers solve defensive woes
Rangers should have been out of sight by the interval but had to wait until an hour in before grabbing the goal that ultimately assured their progress.
They had been defending progressively deeper as Braga began to exert pressure, but Hagi's ball over the top released Kent to race through and fire low past Matheus, in off the far post. It was a counter-attacking masterclass and no more than Rangers deserved, having spurned three glorious first-half chances.
Braga's high defensive line was ripe to be exploited and Rangers picked a hole in it early on. Kent threaded through for Arfield, who bore down on goal before slipping a pass to Florian Kamberi. The striker looked tentative as he struck it and Matheus was able to beat the shot away.
Kent then had an equally gilt-edged opportunity to put Rangers ahead but he dragged his shot wide of the far post from Hagi's pull-back.
Braga were enjoying plenty of possession, particularly in the wide areas, and that looked their most likely route to goal. Twice Nuno Sequeira delivered from the left and twice Paulinho went close - the first header tipped over the bar by Allan McGregor.
But then came Rangers' biggest chance as Raul Silva was penalised for handling Kent's corner - a decision verified by VAR. Hagi, the hero of the first leg, struck the penalty firmly but Matheus threw up his left arm as he dived to his right and kept his team level on the night.
The huge travelling support may have feared those misses would come back to haunt them but Kent's strike settled them.
Rangers' defensive frailties have been exposed domestically this year but they showed a determination and organisation here that have deserted them of late.
Paulinho had one more header, this time off the outside of McGregor's left-hand post, but Rangers held firm to take their place in the last 16.
Man of the match - George Edmundson
Put into the centre of the Rangers defence in place of the beleaguered Nikola Katic, Edmundson was a colossus as he repaid his manager's faith in him.
The entire back-four was solid and the midfield trio of Ryan Jack, Steven Davis and Arfield did a power of closing-down to suffocate Braga's creative forces.
But Edmundson's commanding presence alongside Connor Goldson was the bedrock upon which the victory was built.
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Line-ups
Match Stats
Live Text
Line-ups
Sporting Braga
1Lima Magalhães
36Viana Willemen Da Silva
92CarmoBooked at 47minsSubstituted forRuizat 64'minutesBooked at 90mins
34Melo da SilvaSubstituted fordo Nascimento Galenoat 53'minutes
47de Sousa EsgaioBooked at 89mins
27Rodrigues Barbosa
60Alves Palhinha GonçalvesSubstituted forBarradas Novaisat 45'minutes
5Cruz Jerónimo Sequeira
77Machado Trincão
21da Luz Horta
20Dias Fernandes
Substitutes
3Tormena de Farias
9Ruiz
12Sá
15Luz Horta
17Barradas Novais
18Fonte
90do Nascimento Galeno
Rangers
1McGregor
2Tavernier
6Goldson
4Edmundson
31Barisic
8Jack
10Davis
37Arfield
7HagiSubstituted forAriboat 72'minutes
28KamberiBooked at 73minsSubstituted forOjoat 78'minutes
14Kent
Substitutes
11Ojo
13Foderingham
16Halliday
17Aribo
18Kamara
19Katic
24Stewart
Referee:
Andreas Ekberg
Match Stats
Home TeamSporting BragaAway TeamRangers
Possession
Home70%
Away30%
Shots
Home13
Away9
Shots on Target
Home1
Away5
Corners
Home12
Away4
Fouls
Home10
Away12
Live Text
Posted at
Match ends, Sporting Braga 0, Rangers 1.
Full TimePosted at 90'+5'
Second Half ends, Sporting Braga 0, Rangers 1.
Posted at 90'+4'
Corner, Sporting Braga. Conceded by Scott Arfield.
BookingPosted at 90'+4'
Abel Ruiz (Sporting Braga) is shown the yellow card.
Posted at 90'+3'
Corner, Sporting Braga. Conceded by Allan McGregor.
Posted at 90'+3'
Offside, Rangers. Ryan Jack tries a through ball, but Joe Aribo is caught offside.
Posted at 90'+2'
Corner, Rangers. Conceded by Matheus.
Posted at 90'+2'
Attempt saved. Sheyi Ojo (Rangers) left footed shot from outside the box is saved in the centre of the goal. Assisted by Scott Arfield.
Posted at 90'
Attempt missed. João Novais (Sporting Braga) header from very close range is high and wide to the left. Assisted by Wenderson Galeno with a cross following a corner.
Posted at 90'
Corner, Sporting Braga. Conceded by James Tavernier.
BookingPosted at 89'
Ricardo Esgaio (Sporting Braga) is shown the yellow card for a bad foul.
Posted at 89'
Foul by Ricardo Esgaio (Sporting Braga).
Posted at 89'
Sheyi Ojo (Rangers) wins a free kick on the left wing.
Posted at 88'
Attempt blocked. João Novais (Sporting Braga) right footed shot from outside the box is blocked.
Posted at 87'
Corner, Sporting Braga. Conceded by Ryan Kent.
Posted at 84'
Offside, Rangers. Scott Arfield tries a through ball, but Sheyi Ojo is caught offside.
Posted at 84'
Attempt missed. João Novais (Sporting Braga) right footed shot from outside the box misses to the left following a corner.
Posted at 84'
Corner, Sporting Braga. Conceded by Ryan Kent.
Posted at 81'
Attempt missed. Paulinho (Sporting Braga) header from the centre of the box is too high. Assisted by João Novais with a cross following a set piece situation.
Posted at 80'
Trincão (Sporting Braga) wins a free kick on the right wing.
Posted at 80'
Foul by Borna Barisic (Rangers).
SubstitutionPosted at 78'
Substitution, Rangers. Sheyi Ojo replaces Florian Kamberi.
Posted at 77'
Offside, Rangers. Connor Goldson tries a through ball, but Scott Arfield is caught offside.
Posted at 77'
Attempt saved. Connor Goldson (Rangers) header from the centre of the box is saved in the bottom left corner. Assisted by James Tavernier with a cross.
Posted at 76'
Corner, Rangers. Conceded by Wenderson Galeno.
Posted at 75'
Foul by Wenderson Galeno (Sporting Braga).
Posted at 75'
James Tavernier (Rangers) wins a free kick in the defensive half.
Posted at 74'
Foul by Nuno Sequeira (Sporting Braga).
Posted at 74'
Joe Aribo (Rangers) wins a free kick on the right wing.
BookingPosted at 73'
Florian Kamberi (Rangers) is shown the yellow card for a bad foul.
Posted at 73'
Fransergio (Sporting Braga) wins a free kick in the defensive half.
Posted at 73'
Foul by Florian Kamberi (Rangers).
SubstitutionPosted at 72'
Substitution, Rangers. Joe Aribo replaces Ianis Hagi.
Posted at 71'
Paulinho (Sporting Braga) hits the right post with a header from the centre of the box. Assisted by João Novais with a cross following a corner.
Posted at 71'
Corner, Sporting Braga. Conceded by Scott Arfield.
Posted at 68'
Nuno Sequeira (Sporting Braga) wins a free kick on the left wing.
Posted at 68'
Foul by Ianis Hagi (Rangers).
Posted at 65'
Corner, Rangers. Conceded by Trincão.
SubstitutionPosted at 64'
Substitution, Sporting Braga. Abel Ruiz replaces David Carmo.
Posted at 64'
Attempt missed. Trincão (Sporting Braga) left footed shot from outside the box is close, but misses to the right. Assisted by Fransergio with a headed pass.
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Source: bbc.com