Celtic produced another below-par European performance as they were dumped out of the Champions League.
The home side were heavy favourites to progress, having come back from Slovenia with a 1-1 draw last week.
But they barely tested visiting goalkeeper Jasmin Handanovic in their biggest game of the season.
And Maribor captain Marcos Tavares forced a shot past Craig Gordon on 75 minutes to end hopes of a third successive year in the group stage.
The defeat is a huge blow to Celtic, who will miss out on the £14m they earned in the competition last season as well as the glamour and excitement that accompanies Champions League nights.
The Europa League is scant consolation for Ronny Deila, though after the good fortune that took them past Legia Warsaw by default, there can be little complaint.
Legia crushed Celtic 6-1 on aggregate in previous qualifying round but the Scottish champions were reinstated because the Poles fielded a suspended player in the last few minutes of the second leg.
The Celtic manager and board will come under criticism for a failure to negotiate the qualifying stages successfully, particularly after that earlier reprieve.
The hosts had had ample warning before the solitary goal was scored, but they failed to clear their box and when Ales Mertelj’s shot was blocked, Tavares did brilliantly to scoop the ball over Gordon, who was left clawing at air.
Efe Ambrose, who had almost gifted Jean-Philippe Mendy a second, clattered a header just wide of the post from close range, but that was as close as Celtic came to an equaliser until the final moments when Virgil van Dijk looked on in disbelief as Handanovic superbly saved his stoppage-time shot from eight yards.
A Callum McGregor effort, which came back off the crossbar, marked Celtic’s best period in the match, at the start of the second period, following Kris Commons’ introduction for Beram Kayal.
But, having seen off a first-half storm, Celtic could not make their spell of dominance tell.
Although they seldom found any fluency in the opening 45 minutes, Celtic could easily have been in front early on when Jo Inge Berget’s cross was diverted inches wide of his own goal by Marko Suler.
And, even in the midst of the heavy first-half pressure from Maribor, Van Dijk should have done better than head wide from an Anthony Stokes corner.
Both chances came against the run of play, with Agim Ibraimi and Zeljko Filipovic dictating for the visitors.
For all their possession the team in purple only occasionally threatened Gordon, with Mitja Viler forcing a nervous-looking save, which came back off Tavares and, fortunately for the keeper, back into his arms.
But Tavares and Maribor were to have the last word, as Deila and Celtic count the cost of failure.
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