The result kept Russian champions Spartak third in Group E ahead of their final match, one point behind second-placed Sevilla, who take on group leaders Liverpool later on Tuesday.
Late Maribor goal hits Spartak knockout hopes
The result kept Russian champions Spartak third in Group E ahead of their final match, one point behind second-placed Sevilla.
"For us the glass is half full," Spartak boss Massimo Carrera said. "Today we have done everything we could for the win.
"We created plenty of chances and scored a goal. We gave Maribor almost no chance throughout the match, but the loss of concentration at the very end enabled them to level. It was a goal that we shouldn't have conceded."
Hosts Spartak, spurred on by a capacity 44,000 crowd at Moscow's Otkrytie Arena, found themselves largely frustrated in the first half by resolute defending from their Slovenian opponents.
Maribor full-back Marko Suler missed a chance to put his side into the lead just after the restart when his attempt to convert a free-kick by Dare Vrsic bounced back off the post.
Spartak, desperate for three points to improve their chances of reaching the knockout phase, continued to apply pressure on Maribor, with Ze Luis sending a header narrowly wide on 77 minutes.
But the Cape Verde striker broke the deadlock with eight minutes to play as he tapped in from six yards, beyond helpless Maribor goalkeeper Jasmin Handanovic.
The Moscow outfit failed to see out victory though as Maribor skipper Marcos Tavares found the unmarked Jasmin Mesanovic who snatched a dramatic equaliser two minutes into injury time.
Maribor manager Darko Milanic said he was pleased both with the result and his team's display.
"I'm very happy with our performance," he said. "True, we equalised in the dying seconds, but we had our chances before.
"We played at the highest level. All the players deserve to be applauded because they gave their all on the pitch."
Spartak will most likely need to beat Liverpool in their final Group E encounter at Anfield on December 6 if they are to prolong their Champions League adventure.