The Scottish outfit took a 3-1 lead into the second leg of the third qualifying round, and neither side could add to that as Steven Gerrard's unbeaten start to life as Rangers boss stretched to eight matches.
The hosts did have the chance to force a nervy finale to the match when they were awarded a penalty in the final minute of normal time, but Allan McGregor saved the spot kick to safely see Rangers through.
Maribor seemed to lack the belief that they could overhaul the deficit, resulting in a quiet opening to the match with Rangers more than happy to protect their advantage.
It wasn't until the 18th minute that either side had their first meaningful effort on goal, with Marcos Tavares seeing his snapshot saved by McGregor before Jasmin Mesanovic fired the rebound off target.
The hosts did begin to look more dangerous after that, though, and Luka Zahovic sent one shot over the crossbar before Andy Halliday and James Tavernier both made important clearances in quick succession midway through the half.
A rare sight of goal for Gerrard's visitors saw Connor Goldson header over from a corner, but the home side were soon back on the front foot and Sasa Ivkovic sent a headed effort of his own off target on the half-hour mark.
It took a flying stop from McGregor to keep Maribor at bay with just nine minutes remaining of the half when he got across to keep out Amir Dervisevic's audacious long-range free kick, which looked to be sneaking into the top corner.
McGregor was forced into a more routine stop shortly afterwards to deny Blaz Vrhovec, but it was Rangers who ended the half on top with Alfredo Morelos drawing a first save out of Jasmin Handanovic and Scott Arfield then firing over the crossbar.
The visitors began the second half in similar fashion too when Handanovic was forced to parry away a low shot from Daniel Candeias, although Maribor responded immediately with a chance of their own which was thwarted by a last-ditch block from Goldson.
Jamie Murphy then failed to test the keeper with two sights of goal in quick succession before Rangers began to curb their attacking intent in favour of protecting their two-goal lead from the first leg.
McGregor ensured that it would not be a nervy finale in Slovenia when he spread himself to deny Tavares from point-blank range, and the Brazilian attacker fired another chance wide for the hosts with just four minutes remaining.
Arfield and Morelos also had openings in the closing stages of the match, but the big chance came for Maribor in the final minute of normal time when they were awarded a penalty. Tavares stepped up to take the spot kick, but McGregor saved his effort from 12 yards to kill off Maribor's hopes once and for all.
There was still time for Rangers to almost add insult to injury at the other end when Goldson let fly from outside the area, although his effort fizzed wide as the match ended goalless.
Rangers will now take on Russian outfit FC Ufa in the playoffs.
MARIBOR (4-2-3-1): Handanovic; Suler, Viler, Ivkovic, Klinar (Pihler 52'); Vrhovic, Dervisevic (Dervisevic 73'); Hotic, Tavares, Mesanovic (Mlakar 80'); Zahovic
RANGERS (4-3-3): McGregor; Tavernier, Goldson, Katic, Murphy (McCrorie 76'); Arfield, Jack, Halliday; Ejaria (Kent 68'), Candeias, Morelos