Dereck Kutesa had the home side ahead in the first-half, before Rangers responded early in the second-half through captain James Tavernier.
With a 2-1 victory in last week’s first-leg at Ibrox, Gers progressed in the qualifiers to set-up a repeat of last season’s play-off round against PSV Eindhoven.
From the weekend’s match against Livingston, there were three changes as Ryan Jack and Connor Goldson both returned to the starting XI, while Abdallah Sima also came in from the start, with Leon Balogun, Cyriel Dessers and Sam Lammers on the bench.
Rangers lined-up at Stade De Geneve with Butland in goal and a back four of captain James Tavernier, Connor Goldson, John Souttar and Borna Barisic.
Ryan Jack returned to midfield and was joined there by Jose Cifuentes and Nico Raskin, with Todd Cantwell and Abdallah Sima providing the support for striker Danilo.
It was Cantwell who got the action underway in Geneva and it was a dominant opening period for Rangers as they looked to take control of this second-leg. A Tavernier corner inside the opening five minutes almost provided the opportunity for an early goal as it fell to Jose Cifuentes inside the box but it was blocked by a defender.
In their first attack of the match, Servette showed their threat as a quick move forward saw them break through the Rangers defence as Chris Bedia picked out the run of Timothe Cognat as he drove into the box. One-on-one with Jack Butland, the midfielder sent a powerful shot on target but the Rangers number one matched the effort with a great save, getting a strong hand to the shot.
It was the hosts who took the lead in the 21st minute to level the match on aggregate. A ball over the top opened up the opportunity for Enzo Crivelli to get a strike at goal, it was blocked, but Jeremy Guillemenot controlled it and played it off to Dereck Kutesa. The winger had space and was able to curl a shot beyond Butland and into the top corner of the net.
Rangers had a fantastic opportunity to equalise with half an hour of the match played in Geneva. Todd Cantwell drove forward into the Servette half before feeding the ball out wide into the path of Jose Cifuentes.
The Ecuadorian delivered a great ball into the box with Abdallah Sima and Danilo in the area, however Danilo, who managed to get a touch at the back post was unable to convert from close range.
At the other end, Butland was called in action as Kutesa raced through on goal after linking-up once again with Bedia, but it was another good save from the Rangers goalkeeper as he blocked the shot to deny the home side a second goal of the evening.
Early in the second-half, Rangers had an opportunity to get back ahead in this tie as Cantwell and Danilo linked up, with the former getting a header towards goal but it was held by Joel Mall in the Servette goal.
Shortly after Nico Raskin had a strike from outside the box tipped over the bar by the Servette goalkeeper.
It was a strong start to the second-half for Rangers and the early pressure paid off as they took the lead in this tie once again. Borna Barisic delivered a fantastic ball into the box, and James Tavernier was on hand at the back post to head home.
As the game approached the hour mark, Beale made two changes to his side as Cyriel Dessers and Sam Lammers were introduced in place of Abdallah Sima and Danilo.
Dessers had a good chance to increase Rangers’ advantage shortly after being introduced as he got on the end of a Nico Raskin cross but his header from inside the box was just over the bar.
From a free-kick, Servette captain Steve Rouiller saw a header gathered by Jack Butland as he got on the end of a Timothe Cognat delivery.
Dessers was denied by the post as the game approached the final 10 minutes in Geneva as his low right-footed strike bounced back off the woodwork.
With seven minutes added on at the end of the second-half, Servette continued in their search for a goal with a series of corners, before Lammers saw a shot saved at the other end.
Rangers progress to the next stage of the UEFA Champions League qualifiers and will host PSV Eindhoven at Ibrox next week, before the return leg a week later.
RANGERS: Butland, Tavernier, Goldson, Souttar, Barisic, Cifuentes (Sterling, 84), Jack, Raskin, Sima (Lammers, 61), Cantwell (Dowell, 95), Danilo (Dessers, 61).
Subs: McCrorie, K. Wright, Hagi, S. Wright, Balogun, King, Devine, Lyall.
Servette: Mall, Rouiller, Ondoua (Diba, 71), Cognat, Kutesa (Stevanovic, 71) Mazikou (Baron, 76), Severin, Guillemenot (Fofana, 76), Crivelli, Bedia, Vouilloz.
Subs: Besson, Pfluke, Kaloga, Ronny, Ouattara, Aubert, Touati, Onguene.