Rangers are through to the Champions League play-offs despite defeat to Viktoria Plzen.
Russell Martin's side took a comfortable three-goal lead to the Czech Republic and it proved crucial as the hosts piled on the pressure.
Rafiu Durosinmi beat Jefte to fire in the opener just before half-time and the pressure continued after the break with Rangers also losing Cyriel Dessers to what looked like a serious knee injury.
Lyall Cameron turned in Danilo's ball to level the tie on the night, but after a string of impressive saves Jack Butland couldn't keep Svetozar Markovic's header out
The Ibrox side are now just a two-legged tie against Club Brugge away from the prestige and prize money of the League Phase in Europe's elite tournament.
The first leg is at Ibrox on Tuesday August 19 with the return in Belgium a week later.
Rangers do enough to progress
After a tough test from Panathinaikos in the previous round, Martin brought captain James Tavernier and Nico Raskin back into the starting line-up as he warned his players the tie was far from over.
The team coped with the pressure in the Doosan Arena in the early exchanges but fell behind in the 41st minute when slack play from Jefte saw Amar Memic fire across the box for Durosinmi to slam home.
After the worry of losing Dessers to injury, Cameron restored their three-goal cushion with his first goal for his new club after a brilliant pass from substitute Danilo.
The hosts continued to pile on the pressure with Rangers surviving a number of late scares.
Butland produced a string of saves but was left helpless when Markovic was left with all the space he wanted to nod home a late consolation.
Martin looking for more 'aggression' from Rangers
Rangers head coach Russell Martin speaking to BBC Radio Scotland:
"I am really pleased with that.
"There were some good moments in the game we didn't make the most of, but I'm disappointed with the number of shots and chances they have and most of it's self-inflicted.
"Our level of quality on the ball and decision making wasn't good enough.
"If we are not as clean with the ball as we should be, we have to be more aggressive.
"We have a lot to work on, but we're through. Both goals are outrageous and we have to defend better, but we defend more than we should have because we are sloppy with the ball."
On substitutes Kieran Dowell, Nadim Bajrami and Danilo, he added:
"Dani really helped us with the ball, the way he took it in, and he was so clean and he deserved to get on the end of some of the moves where the final balls through to him were not good enough.
"That summed up our night. We broke through the press relentlessly in the first half, played into the front really quickly, much earlier than the weekend. But, when we get there, the ball gets turned over and we are defending again.
"I don't mind losing the ball in their half if we are being so aggressive, but it was sloppy little details."
Boyd: A 'worry' for Martin
Sky Sports' Kris Boyd:
"When you get to this stage the main thing is just to get through but once again it'd be a worry for me and it will be a worry for Russell Martin.
"The two goals that Rangers conceded were really poor defensively, Jefte for the first one and then it looked as if he got off the back of [Joe] Rothwell for the second one, which would be a worry.
"You know Rangers are conceding goals but Lyall Cameron, his first goal for Rangers, he will be absolutely delighted.
"The work was done in the first leg but managed to get that away goal that you know settled Rangers down again because Plzen did have a few chances to go back to 1-1 but they were comfortable enough."
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