Roared on by 7,000 fervent home fans in their Pionir Arena, Red Star overturned a nine-point second-half deficit as forward Marko Guduric turned out to be a trump card.
Playing in his first senior season, 20-year-old Guduric sank nine of his 16 points in the fourth quarter after Bayern Munich had wiped out the home side's 31-20 first-quarter lead.
"I couldn't imagine in my wildest dreams that I'd be the one to turn the tide in a match as big as this one," Guduric told Reuters courtside as jubilant fans chanted his name.
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"We didn't roll over despite being on the ropes at the end of the third quarter and I hope we will give our fantastic fans more to cheer about in the second group stage."
The Top 16 features two pools of eight teams playing each other home and away on a round-robin basis.
Red Star became the last team to advance, at Bayern's expense, after the battling visitors cracked under pressure in one of European basketball's most intimidating venues.
Red Star nailed four of their opening six three-pointers but aggressive Bayern defending stifled their long-range artillery in the second and third quarter.
Guduric and American forward Quincy Miller then galvanised the crowd with a barrage of long-range shots, the latter also hitting a vicious slam-dunk, and the home side never looked back after nosing ahead 74-73 with three minutes left.
Miller finished with a game-high 21 points and 10 rebounds and German centre Maik Zirbes added 17 for Red Star, while Serbian forward Dusko Savanovic led Bayern with 19 points.
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