The result left Russian champions Spartak third in the group on six points from five games, two behind leaders Liverpool and one adrift of second-placed Sevilla, who play later on Tuesday.
The home side dominated throughout but were unable to break down a packed and well-organised Maribor defence until the 83rd minute when Ze Luis scrambled the ball past keeper Jasmin Handanovic from seven metres.
Just when it seemed Spartak were home and dry, late Maribor substitute Jasmin Mesanovic stroked the ball into an empty net after Marcos Tavares broke down the right and delivered a fizzing low cross which left the home team's defence flat-footed.
Despite Spartak's incessant pressure, it was the visitors who missed the game's best chance when central defender Marko Suler hit the post in the 50th minute after halftime substitute Dare Vrsic floated in an inviting free kick.
Ze Luis sliced a header off target in the first half and powered another one inches wide of the near post in the 77th minute before he finally found the net following a goal-mouth scramble to thrill the fervent home crowd.
The Spartak faithful, however, were left stunned in the second minute of stoppage time after keeper Alexander Selikhov failed to cut out Tavares's cross, leaving Mesanovic with the simplest of tap-ins from five metres.
Having also been held to a 1-1 draw by Maribor in the reverse fixture, Spartak must now win their final group match at Liverpool next month if they are to avoid dropping into the second-tier Europa League after the winter break.
(Writing by Zoran Milosavljevic in Belgrade; Editing by Toby Davis)
