Gers eventually levelled through Carlos Bocanegra but his strike came with time to get a winner inside 90 minutes rapidly frittering away.
Mo EduAnd when a second strike for the hosts would have forced extra time, it wasn’t to come as the visitors hung on.
Ally McCoist’s men probably deserved more than what they finished with as they created plenty of chances to win the tie outright.
But their failure to convert in front of goal was a huge disappointment and they must focus on the league again for now.
McCoist has only seen his team win three out of eight competitive fixtures so far this term and that will be a big concern to him.
He isn’t the only SPL manager with a failed Euro campaign to look back on as both Celtic and Hearts also slipped out of the competition tonight.
Even so, his focus will only be on his own side and he must now pick his men up for Sunday’s league clash with Aberdeen.
After a handsome 3-0 weekend win at Motherwell, boss McCoist made three changes to his team with one of those enforced.
Steven Naismith missed out through suspension after a second European booking of the campaign in Slovenia last week and his place was taken by Maurice Edu.
Jordan McMillan also dropped out with a calf strain and Ross Perry took a place on the bench, meaning Kirk Broadfoot and Bocanegra made returns.
Both sides made a tentative start but after there was outcry at Juan Ortiz not getting a penalty when he merely fell over, the match quickly burst into life.
Steven Davis had the first real chance of the fixture as his long-range shot was deflected wide and Nikica Jelavic headed the resulting corner wide of the target.
Gregg Wylde’s direct running and pace also caused problems for the away rearguard and in the early stages they struggled to contain him.
Dorin GoianMaribor, of course, turned up in Glasgow protecting a 2-1 lead but they were anything but content to sit on it.
Indeed, Agim Ibraimi – the scorer of their first goal at the Stadion Ljudski vrt seven days ago – should really have netted again instead of screwing high and wide.
Back came Gers, with a Davis corner almost sneaking in after it came off Edu’s face and another header from the American landing in keeper Jasmin Handanovic’s arms.
The Light Blues were certainly on top and were getting a decision or two their way too, with a clear foul by Lee Wallace unpunished by referee Aleksandar Stavrev.
But they couldn’t yet make a breakthrough, with Lafferty denied by the onrushing Handanovic after he was played in by Jelavic.
The Ulsterman was close to making the difference again moments later as good interplay with Edu led to him curling just around the post from 20 yards.
Dorin Goian, so impressive at times as he marshalled the defence with such composure, also smashed a drive in from long range but it was a couple of feet wide.
With so many opportunities being spurned, the first half was quickly turning into one of frustration for Rangers.
That was only enhanced six minutes before the break when Wallace had to be replaced by youngster Perry in the back line.
Jelavic hit the target but found Handanovic equal to him again with a header from a Wylde free kick.
And Lafferty was too slack with a glorious chance when he had just the keeper to beat as he shot straight at him.
The midway point left Gers with pressure on them slowly building after a decent showing to that point had left them without any rewards for their efforts.
But McCoist kept faith with the same team which had finished the opening period and Nejc Potokar had to react well to keep the scoresheet blank with a sharp clearance from Broadfoot.
Ally McCoistDavis also chose to pick out a man when it seemed easier to score after great build-up play down the right and once again there were gasps of irritation from the stands.
And then, with that, Maribor took the lead in controversial circumstances as they scored from a free kick which should never have been given.
Broadfoot was penalised for winning a header fairly but it was taken quickly all the same and with the defence out of position, they were swiftly caught out.
Goian gave chase and with Perry in limbo too the ball was threaded through to Volas, who shot past McGregor from 15 yards.
Dejan Mezga nearly added a second as the Slovenians poured forward again and with little more than half an hour to go, Rangers suddenly looked bereft of ideas.
They desperately needed to level and quickly but Broadfoot’s trundling ball across the face of goal was missed by everyone before Wylde eventually poked it past.
Bocanegra saw his header deflected behind as the hosts lay siege to their opponents’ goal and Lafferty scuffed a half volley into the ground when he should have done far better.
McCoist threw on David Healy for the quiet Ortiz in a bid to change things but with only quarter of the game left, there was still much to do.
There was what seemed to be a good penalty claim as a ball in from Wylde was touched by the Northern Ireland striker on to Aleksander Rajcevic’s hand but it wasn’t given.
As another Jelavic header was gathered comfortably by Handanovic, it seemed it wasn’t going to be the SPL champions’ night.
Carlos BocanegraGers were certainly getting closer, with Perry’s shot diverted the wrong side of the post before they finally made it 1-1.
And with quarter of an hour remaining, it was Bocanegra who grabbed a home debut goal on the turn after Wylde’s corner was knocked down by Jelavic.
Suddenly it was game on and Jelavic scarpered forward but chose the wrong option when he picked out Wylde rather than Healy.
The ex-Sunderland star then saw the whites of Handanovic’s eyes when he was found by Lafferty but the keeper saved well.
Goian headed wide as the Light Blues cranked up the pressure but Maribor did their best to tone things down again, taking every chance they could to break up the rhythm of the game.
Sadly it worked, with any impetus Gers had after finally regaining equality on the night quickly fading.
Five minutes of added time were added and with that came renewed hope but Goian was off target once more and Wylde shot past too.
Any hope of a dramatic recovery was gone and now Rangers must concentrate only on their domestic campaign in the months ahead.