Goals from Nacho Novo and Fernando Ricksen gave Rangers a vital one-goal lead after a hard-working victory over Anorthosis Famagusta in Cyprus.
Both sides had squandered chances before Novo pounced to fire home after a good save by Antonis Georgallides denied Ricksen.
Ricksen slotted in the second in the Champions League qualifier first leg.
But, within seconds, poor control from Julien Rodriguez allowed Nicolaus Frousos to drill in a quick reply.
New signing Rodriguez had been given his chance in defence along with Michael Ball, with Ricksen and Ian Murray moving into midfield at the expense of Peter Lovenkrands and Alex Rae.
Rangers' more defensive line-up were under pressure as Anorthosis, without Nicolaos Katsavakis after the Greek defender was suspended for being dismissed in the defeat of Trabzonspor, started the third qualifying round tie at a hectic pace.
But Rangers were first to seriously threaten, a snap shot from just outside the box by Novo forcing goalkeeper Georgallides to push the effort wide at full stretch.
Novo set up Ian Murray 12 yards out, but the former Hibernian defender skied his shot well over the bar.
Anorthosis came back into the game and Frousos stole behind the Rangers defence only to see his chested flick over goalkeeper Ronald Waterreus slip a yard wide.
The striker missed another great chance when he beat Marvin Andrews to a ball behind the defence but sent his chip over the keeper off the face of the post.
Waterreus palmed away a powerful free-kick from Anorthosis player-coach Temuri Ketsbaia on the stroke of half-time.
Rangers had been forced into a containing game after the break until they broke forward to take a 65th-minute lead.
Georgallides did superbly to palm clear a Ricksen overhead-kick from 10 yards out and Novo pounced to fire the ball into the top corner of the net.
Waterreus prevented a quick equaliser, diving at full stretch to turn a low Koba drive wide of the post.
Ricksen was then found by a fine Dado Prso ball behind the Anorthosis defence and the Dutch midfielder slipped the ball under the advancing goalkeeper for the second.
Anorthosis looked downhearted but were allowed back into the game when Rodriguez let the ball bounce off his thigh and Frousos fired home from just outside the box.
And Waterreus saved well with his feet to deny substitute Kampantais a late equaliser.
Anorthosis Famagusta: Georgallides, Poursaitides (Tsolakides 74), Haxhi, Louka, Xenidis, Maragos (Konstantinou 83), Frousos, Kinkladze, Ketsbaia, Tsitaishvili (Kampantais 70), Nicolaou.
Subs Not Used: Kokkinos, Markou, Samaras, Parmakis.
Booked: Xenidis, Haxhi.
Goal: Frousos 72.
Rangers: Waterreus, Pierre-Fanfan, Andrews, Rodriguez, Ball, Ricksen, Ferguson, Murray, Buffel (Lovenkrands 58), Novo (Burke 79), Prso (Thompson 74).
Subs Not Used: Klos, Malcolm, Alex Rae, McCormack.
Booked: Ball, Ricksen, Andrews.
Goals: Novo 64, Ricksen 71.
Ref: Frank De Bleeckere (Belgium)