After a dour opening period in Glasgow, second-half goals from Scott Arfield and James Tavernier ensured Steven Gerrard's team will be involved in Friday's the draw.
Connor Goldson saw Christian Luyindama nod his header over the bar before Borna Barisic volleyed a cross from Ryan Babel behind just as Sofiane Feghouli looked to steal in during a first half of few openings.
The deadlock was broken in the 52nd minute, though. Alfredo Morelos dummied Tavernier's pass and Ianis Hagi steered the ball in behind for Arfield, who guided a cool finish with the outside of his boot beyond Fatih Ozturk.
Rangers doubled their lead seven minutes later when Tavernier rose above Martin Linnes at the back post to head home Barisic's deflected cross.
Younes Belhanda was booked for remonstrating with referee Andris Treimanis after his appeal for a penalty following a tackle from Arfield on the edge of the box was ignored.
Morelos missed a great chance to improve Rangers' advantage and they were dragged into a tense finale when Marcao's header found a way past Allan McGregor and Ryan Jack in the 87th minute.
However, Gerrard's men held on to ensure their European adventure will continue.