Juan Manuel Ortiz netted his first goal for Rangers when he fired the Glasgow giants into a first-half lead, but Agim Ibraimi levelled after the break before substitute Etien Velikonja found the back of the net in injury time.
Rangers must now hope they can rescue the tie at Ibrox and book their place in the group stages following the disappointment of crashing out of Champions League qualifying.
Carlos Bocanegra was handed his Rangers debut from the start after signing from St Etienne on Tuesday night as boss Ally McCoist made a dramatic late swoop to add to his squad ahead of UEFA's signing deadline.
The United States skipper was granted international clearance just hours before the clash in Slovenia, allowing him to partner Dorin Goian in the heart of defence.
Lee McCulloch was added to the side after recovering from a knee injury, while Kyle Lafferty was named on the bench for the first time this season following a hernia operation.
Maribor were without captain Marcos Tavares, who failed to recover from a back problem in time.
Rangers found themselves under pressure early on when an error from Bocanegra allowed Ales Mertelj to unleash a shot which was blocked by keeper Allan McGregor.
At the other end, Nikica Jelavic had the chance to find the back of the net when a corner broke to him in front of goal but his first effort was blocked before he fired wide from the rebound.
Jelavic then attempted to turn provider for Ortiz with a tempting cross from the right but the danger was cleared before he could connect from six yards out.
The home side had enjoyed much of the possession without really taking advantage and they found themselves trailing when Rangers surged into the lead after 31 minutes thanks to Ortiz.
The Spaniard started the move by finding Kirk Broadfoot out on the right flank, before racing into the box where he was waiting to collect the return pass and flick home from six yards.
Steven Naismith picked up the first booking of the game six minutes later for a challenge on Mitja Viler, before Dejan Mezga saw his free-kick swerve inches past the post after Maurice Edu had conceded a foul on the edge of the area.
Naismith was withdrawn at half-time, with McCoist perhaps mindful of the two red cards his side picked up against Malmo, allowing Lafferty to make his first appearance this term.
Maribor were back on level terms after 52 minutes when Ibraimi collected on the corner of the box from a throw-in and sent a powerful left-foot shot past McGregor.
Rangers could have restored their lead when Jelavic set up the shot for Edu but he looked on in frustration as his drive from distance fell just wide of the target.
Jelavic felt he was held in the box by Arghus Soares Bordignon and an angry exchange of words took place between the two players as the action raged on at the other end of the park.
Maribor had the chance to put their visitors under pressure with a free-kick 25 yards out and, again, Mezga was not too far away with an effort that fizzed past McGregor's left-hand post.
Rangers had the chance to challenge with a set-piece of their own and Jelavic nodded narrowly past the upright after connecting with Lee Wallace's corner.
But it was Maribor who had the net bulging in injury time when Mezga teed up substitute Velikonja, who back-heeled the ball over the line.