Simone Biles remains peerless. Even when she's not quite perfect.

The American gymnastics star edged Brazil's Rebeca Andrade during a tense Olympic all-around final on Thursday, with Tokyo gold medallist Sunisa Lee third.

Biles' total of 59.131 was just over a point ahead of Andrade at 57.932, one of the closest calls Biles has ever endured at a major international event.

The margin was the smallest in a major international event since Biles captured the third of her record six world championships in 2015.

She was a teenager then. She's an icon now.

The 27-year-old who is redefining what a gymnast can do - and just as notably, for how long she can do it - is the third woman to become a two-time Olympic champion, joining Larisa Latynina and Vera Caslavska.

Biles also is the oldest woman to claim the biggest title in her sport since 30-year-old Maria Gorokhovskaya, of the Soviet Union, won the first-ever Olympic all-around in Melbourne in 1952.

Yet Biles' sixth gold and ninth overall medal - the same as Romanian great Nadia Comaneci, who was among the star-studded crowd - did not come as easy as so many that came before.

She misjudged a transition on uneven bars, the weakest of her four events, letting go of the upper bar too soon and forcing her to reach for a larger-than-expect gap.

While she didn't fall - Biles muscled her way back into the routine - it blunted her momentum and led to major deductions that left her trailing Andrade through two rotations.

The deficit didn't last.

Biles responded with a largely wobble-free 14.566 on the balance beam, the best beam score of the night, while Andrade was forced to do a major balance check, dropping her to second.

On the floor - Biles' signature event - the American performed a 75-second set including music from Taylor Swift and Beyonce, featuring the hardest tumbling ever done by a woman in the sport's history.

When she was done - sealing gold that served as a redemption of sorts three years after pulling out of multiple finals in Tokyo to focus on her mental health - Biles sprinted to hug Lee just off the podium.

Lee earned bronze despite spending much of the last 15 months dealing with multiple kidney diseases that left her return to the Games very much in doubt.

Biles could still win more at this Games, in three event finals, yet she is already in the conversation as perhaps the greatest American Olympian ever.

Biles is no longer the prodigy who triumphed in Rio de Janeiro eight years ago.

She's married and a vocal advocate for survivors of sexual abuse and the importance of proper mental health.

She has said repeatedly over the last three years that what happened in Tokyo is a part of her past, not a part of her present, and if critics have a problem with it, that's their issue, not hers.

She's moved on to bigger things. Like setting a standard that may never be reached - in her sport, and maybe all others, too.

With AAP.