Rafiu Durosinmi opened the scoring for the Czech side before Lyall Cameron netted his first Rangers goal in the second-half to level the game on the night.
The home side restored their lead in the final 10 minutes through Svetozar Marković, but Rangers' performance over the two ties earned a place in the next qualifying round.
There were two changes from last week’s first-leg as captain James Tavernier returned in place of the injured Max Aarons, while Nico Raskin came into midfield and Joe Rothwell was named on the bench.
Rangers started with Jack Butland in goal behind a back four of James Tavernier, Nasser Djiga, John Souttar and Jefte. Raskin joins Mohamed Diomande and Lyall Cameron in midfield, while Cyriel Dessers is supported by Oliver Antman and Djeidi Gassama.
Rangers of course, had their three-goal advantage from last week’s match at Ibrox, but Russell Martin knew he needed another big performance from his side to ensure a spot in the play-off.
It was a fairly open start at the Doosan Arena, as the hosts were looking to threaten early on and find a route back into the tie.
Jefte had the first strike at goal for Rangers as he drove into the Plzen half before getting a shot away but his low effort was held comfortably by Martin Jedlička.
At the other end a corner opened up the opportunity for the hosts as captain Matěj Vydra sent a header towards the Rangers goal which was deflected out for another corner. From the second set-piece, the ball broke for Amar Memić outside the box and he released a curling right-footed strike towards goal which bounced just wide of Butland’s post.
Another shot from the edge of the box, this time from Lukáš Červ, was pushed away by the Rangers number one as the home side continued to look for a goal.
In a nice move from Rangers, Martin’s men broke forward with Gassama, Antman and Dessers combining, before James Tavernier delivered a cross into the box. Lyall Cameron got on the end of it and tried to lift a right-footed shot over the keeper but it was just high of the target.
With 37 minutes played, the home side had a big chance as the ball was played through to Prince Kwabena Adu and he raced towards the Rangers goal. With James Tavernier alert to the threat, the captain did enough to put pressure on the forward, who sent his shot wide of the target.
However, it wasn’t long until the Czech side did take the lead, and get a goal back in the tie. Amar Memić controlled the ball at the byline before picking out Rafiu Durosinmi inside the box and he sent a powerful first-time hit beyond Butland and into the back of the net.
Durosinmi came close again before the break as he headed a Karel Spáčil cross towards goal, but it was held by Butland.
In the second-half, Amar Memić drilled a shot just wide of the post, before Prince Kwabena Adu saw a header gathered by Butland. Rangers were forced into a change with 54 minutes played as Cyriel Dessers came off with an injury and was replaced by Danilo.
With half an hour to go, Gers restored their three-goal lead in this tie and drew level on the night, and it was a first Rangers goal for Lyall Cameron. Diomande picked the ball up on the byline and sent it back into the box in search of Danilo, the striker had a shot, which Cameron managed to get a touch on to send it beyond the goalkeeper.
Russell Martin turned to his bench again in the 68th minute as Kieran Dowell and Joe Rothwell came into midfield in place of Mohamed Diomande and Lyall Cameron.
Milan Havel headed just wide for Viktoria Plzen as the game entered the final 20 minutes, before Jack Butland was called into action with a good save to deny Price Kwabena Adu.
There was another goal back for the home side with 82 minutes on the clock, as substitute Svetozar Marković found the target with a header after a deep cross from the far side of the box, but it was Rangers who progressed to the play-off round which will start with a home tie at Ibrox next Tuesday.
RANGERS: Butland, Tavernier, Djiga, Souttar, Jefte, Raskin, Diomande (Rothwell, 69), Cameron (Dowell, 69), Antman (Bajrami, 86), Gassama (Cortes, 86), Dessers (Danilo 54).
Subs: Kelly, Fernandez, Gentles, Rice, Curtis, Hutton.
Viktoria Plzen: Jedlička, Spáčil (Ladra, 69), Červ, Vydra, Durosinmi (Kabongo, 69) , Jemelka, Paluska, Valenta, Dweh (Marković, 57), Adu, Memić (Havel, 69). Subs: Tvrdoň, Wiegele, Višinsky, Doski, Souaré, Panoš, Slončík