Rangers will need to come from behind in Glasgow if they are to reach the semi-finals of the Europa League.
The difference in front of a thunderous crowd was the effort by Abel Ruiz just before the break.
The reigning Scottish champions struggled to create and failed to register an effort on target against their highly-charged hosts.
The sides will meet next week.
The winner of the tie will face either Atalanta orRB Leipzig in the last four.
The Municipal Stadium in Braga was climbed in hopes and expectation.
Two years ago, Rangers won in the hills above the Portuguese city to reach the last 16. Over 10,000 followed the Scottish champion back here again, the blow of Sunday's Old Firm defeat did little to diminish their spirits as they made the trip up Monte Castro on an overcast and gloomy night.
The uphill climb is symbolic of the challenge the team face after the first leg.
Rangers, who at times toiled without the focal point of the injured Alfredo Morelos, were overwhelmed by Braga.
At the beginning, there was a sense of formality. The smoke from the fireworks dissipating made it possible to see a giant fan display beneath them from the locals.
The hills were alive with the sound of a bumper home crowd clapping in unison, their appetite whetted for another barnstorming performance. They were not disappointed.
Rangers started well. Ryan Kent and Fashion Sakala had half chances in quick succession, with the former slaloming by a clutch of defenders five minutes later. The hosts would soon find their rhythm.
The shots came in waves. They applauded every time Braga crossed. On 25 minutes, a collective gasp rose into the Portuguese sky, as the hosts' top scorer, Ricardo Horta, slashed a low shot off the left-hand post.
Number two came next. As his shot went through the net, he thought he had scored, sparking bedlam in the stands. The party had stopped when the referee ruled that Ryan Jack had been tripped in the build-up.
As the Rangers support tried to rouse their side from the gods, a youthful Braga continued to come. Kent burst forward on the break, but was snuffed out, while Sakala's shot was well over the bar when a clear and rare sight of goal had creaked open.
The hosts took the lead on 39 minutes.
Iuri Medeiros made a play on the ball as Leon Balogun failed to clear it. The former Barcelona man sent the ball thundering past the helpless McGregor after taking one measured touch.
The break did little to stop the hosts being roared on from the loud stands, as Van Bronckhorst wasted no time heading down the tunnel.
Carlos Carvalhal's Braga smothered any attempt to cleave them open, even though McGregor wasn't tested all that often.
Kemar Roofe, Joe Aribo and Borna Barisic were introduced in a bold roll of the dice as Rangers pushed. The defender couldn't get a toe to a dropping ball in injury time, and aConnor Goldson headed wide of the far post from a corner when he should have done better.
The hosts, who defeated Benfica last week, will feel good about their trip to Glasgow next week.
That this team has quality.
They have already taken a few scalps this season, but they dominated most of the game. Rangers struggled to cope with the high press in the second half, and their interplay was excellent.
They are the most attacking team in the league, according to their manager. It was seen in spades here.
It was quite different for Rangers. It was the first time in Europe that a shot was not registered on target since 2009.
The travelling fans were confident that their team would cope without Morelos. Tonight's answer will be a worry.
They are still in this tie and can return to Scotland to turn this around. They need to be better than they were here.
The Rangers are playing big games. A must-win game against St Mirren in Paisley is on Sunday at 12:00 and a game against Braga in Glasgow on Thursday at 20:00.
Formation 3-4-3.
70de Souza Silva16Veiga Teixeira Carmo3Tormena de Farias2Couto8Al Musrati10Luz Horta57Martins Gomes45Picanço Medeiros9Ruiz21da Luz HortaFormation 4-3-3.
2Tavernier6Goldson26Balogun3BasseyThe match ended with Rangers not winning.
The second half ended with Rangers 0.
The hand ball was by Fabiano.
Calvin Bassey (Rangers) had a foul.
The free kick was won in the attacking half.
Corner, Rangers. David Carmo was the one who Conceded.
The attempt was blocked. Calvin Bassey's shot from the centre of the box is blocked. John Lundstram assisted.
There is a substitution for Sporting Braga. There is a new person in place ofYan Couto.
The right wing is where the free kick was won byConnor Goldson.
David Carmo had a foul.
Kemar Roofe won a free kick.
Castro had a foul.
It was an attempt, Rangers. James Tavernier tried a through ball, but Kemar Roofe caught it.
Foul by Kemar Roofe.
The defensive half is where Matheus won the free kick.
There is a substitution for Sporting Braga. Castro replaces Al Musrati because of an injury.
There is a substitution for Sporting Braga. Lucas Mineiro replaces Andr.
The corner is Sporting Braga. They had a match with Allan McGregor.
The attempt was saved. Horta's shot from outside the box is saved in the bottom left corner. It was assisted by Rodrigo Gomes.
The defensive half is where Glen Kamara won the free kick.
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