Ryan Kent scored the only goal of the game in Braga to send Rangers into the last 16 of the Europa League on Wednesday.
The Scottish giants advanced 4-2 on aggregate after coming from 2-0 down at home in Glasgow last week to win the first leg 3-2.
Ianis Hagi, who netted twice in that comeback, missed a penalty just before halftime in Portugal but then set up Kent for the winner in the 61st minute.
Romanian Hagi launched a ball over Braga's high line for Kent to run onto, and the forward drilled a left-footed finish into the corner.
"There have been a lot of opinions on Ryan of late on what type of form he is in," Rangers manager Steven Gerrard said.
"People don't give him the credit he deserves in terms of the amount of running he does for us - but he came big for the team and scored the important goal.
"The players have been outstanding to a man over both games. I'm really proud of them for getting the job done."
It was the only round of 32 game to be played ahead of Thursday's regular schedule, when Braga's Portuguese rival Porto play at home to Germany's Bayer Leverkusen.
Australian Associated Press