The 17-year-old French-born athlete took the title ahead of China's Qiu Qiyuan, who took the world title ahead of the Algerian last year, 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 the Olympic champion. I'm speechless," said Nemour.
"It was my ultimate dream, years of hard work, details. I'm honoured to have been able to win this medal, first of all for me and for Algeria too."
Nemour's stunning high-flying acrobatic performance earned a career-best 15.700 points to push Qiu, also 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 two years ago, after the French federation blocked her from competing after a medical dispute.
A growth spurt of 14 centimetres (5.5 inches) in a year just after she turned 13 caused a bone problem which required surgery on both knees.
'Intensive road'
After a legal battle lasting several months Nemour was excluded from the France team and switched to competing for Algeria at worlds last October, and the Olympic Games in Paris.
"I am very happy to have won this medal for Algeria. I hope I made them proud," she said.
"It has been an intensive road. But right now I am glad I performed well and have the gold."
Nemour was the favourite in the absence of US gymnastics great Simone Biles who failed to qualify for the uneven bars final.
But competing last, teammate Lee grabbed bronze ahead of Derwael, a former two-time world champion who was returning after surgery.
"Having seen the others doing so well kind of put the pressure on me to do a good routine," said Lee, 21.
"That's exactly what I did."
Her routine earned 14.800 points and her third medal in Paris after team gold and bronze in the all-around.
For Qui there were "regrets" at missing out on gold.
"(Kaylia) did amazing today," she said. "All the movements were so smooth. Her routine was perfect. She did even better than her previous routines."
