The 18-year-old Olympic debutant, who helped the USA win team silver on Tuesday, finished on 57.433.
Brazil's Rebeca Andrade won silver and Russian Angelina Melnikova bronze.
Jessica Gadirova's 10th place was the best result ever by a British woman in the event.
Andrade's score of 57.298 secured Brazil's first ever women's gymnastics medal at the Games, while Melnikova took bronze with 57.199.
"It's my first world ranking, so I know where I am and where I stand," said 16-year-old Gadirova, whose twin sister Jennifer finished 13th.