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.
"Over the years hopefully I will just grow. I've got a few days to rest the legs up ready for the floor final [on Monday]."
The twins helped Great Britain win a historic team bronze on Tuesday and Jennifer may yet join Jessica in Monday's floor final if Biles withdraws.
Biles withdrew from the team final on Tuesday and later announced she would not compete in the all-around final either, but the four-time Olympic gold medallist enthusiastically cheered on her fellow gymnasts from the stands.
The 24-year-old has yet to confirm whether she will compete in the individual apparatus finals, which start on Sunday, saying she will take "each day as it comes".
After Biles withdrew from the team final, Lee said the Olympic star "carries the team basically", but the teenager has shown she is ready to take star billing.
Lee broke her foot in June 2020 but concerns over her floor routine after the injury proved unfounded as the American's score of 13.700 was enough for gold in a highly competitive final.
American Cup-winning artistic gymnast Katelyn Ohashi said on BBC Radio 5 Live that Lee had proved "she's a real competitor", adding: "She's followed in the footsteps of Simone."
Brazil's Andrade has had her own injury struggles, with the 22-year-old suffering a third serious knee injury in four years in 2019.
She led at the halfway stage, but errors on the floor - her final apparatus - saw Lee pip her to gold.