The 17-year-old French-born athlete took the title ahead of China's Qiu Qiyuan with American Sunisa Lee snatching bronze. Defending champion Nina Derwael of Belgium finished fourth.
"I'm so shocked, it's the dream of all my life. I can't believe it has happened, I'm speechless," said Nemour.
Nemour's stunning high-flying acrobatic performance earned 15.700 points to push world champion Qiu, 17, into the silver medal position with 15.500.
"In qualifying I had 15.600, when I saw her 15.500 I said, I really had to fight and gave the performance of my life," said the Algerian.
"It's crazy, I'm honoured to have this medal after all that has happened, it's a relief."
Nemour switched to represent her father's country after the French federation blocked her from competing on medical grounds after a dispute.
US gymnastics great Simone Biles failed to qualify for the uneven bars final.
But competing last, teammate Lee snatched bronze ahead of Derwael, a former two-time world champion who was returning after surgery.
