Simone Biles’s third and perhaps last Olympic Games came to an end on Monday afternoon with the floor exercise final, where she was pipped by Brazilian rival Rebeca Andrade for the gold by 0.033 points.

The 27-year-old, the most decorated women’s gymnast ever and the oldest American woman to make an Olympic gymnastics team since the 1950s, added a fourth medal at these Paris Games after previous golds in the team event, the all-around and the vault. She has now won 11 medals in an extraordinary Olympic career spanning eight years.

Competing third to last of the nine finalists, Biles was given a standing ovation after an extraordinary routine where she completed the eponymous Biles II triple double on the first pass and a Biles I double layout with half twist on the third, but was dinged by deductions for stepping out of bounds that left her 0.033 behind Andrade.

Jordan Chiles of the United States took the bronze, climbing from fifth to third after an inquiry. She was reduced to tears of joy after her updated score of 13.766 flashed on the screen, only 0.066 points clear of the Romanian pair of Ana Barbosu and Sabrina Maneca-Voinea.

Biles extended her mark as the most decorated women’s gymnast ever, with a combined 41 medals between the Olympics and world championships.

“I can’t be more proud of how I’ve done,” she said afterwards. “I’m 27 years old walking away from this Games with four medals to add to my collection. Not mad about it.”

With a second career gold to add to her three silvers and one bronze, the popular Andrade became the most decorated Brazilian Olympian ever. Andrade’s other gold came at Tokyo 2020 in the vault after Biles pulled out.

Earlier Biles had missed out on her fourth medal in the balance beam on Monday after she fell during her routine and finished in fifth place, one position ahead of her US teammate Suni Lee, who also fell.

Meanwhile, Italy’s Alice D’Amato didn’t win that final so much as survive it. But a routine that avoided major errors turned out to be enough for the 21-year-old from Brescia to win an improbable Olympic title, her country’s first ever gold medal in artistic gymnastics, sharing the podium with teammate Manila Esposito, who earned bronze. Biles finished fifth with an identical score to Lee, while Chinese teenager Zhou Yaqin took silver.

On the final day of a meet that began seven days ago with Italy capturing their first team medal in artistic gymnastics in 96 years, D’Amato and Esposito managed to hold their nerve while one heralded rival after another made costly mistakes in a beam final whose footage won’t be sent to the Olympic Museum in Lausanne for posterity.

The beam, which dares gymnasts to perform routines of extraordinary rigour on a platform 4ft above the ground and not much wider than a credit card, is the sport’s most precarious apparatus. On Monday in what can only be described as one of those days, at least half of the eight finalists fell victim to the discipline’s essential unpredictability.

Competing first in the running order of eight was Zhou, the 18-year-old Olympic debutante who took silver on beam behind Biles at last year’s worlds, who was on her way to a flawless routine before a balance check that forced her to bend over and grab the beam, drawing audible gasps from the crowd and a significant deduction from the judges. Her score of 14.100 was a disappointment after qualifying highest with 14.866.

Next was Lee, who put together a solid set until slipping on the last skill of her aerial series and splitting the beam in what appeared to be a very painful fall. She was consoled by longtime coach Jess Graba after completing her set for a score of 13.100, ending her Paris Games with a team gold and two bronzes, including one in the all-around, no minor haul for a gymnast who overcame a pair of career-threatening kidney ailments just to reach the starting line.

The door was suddenly open for Biles to become the third Olympic beam champion from the United States after Shannon Miller and Shawn Johnson.

But first D’Amato took to the apparatus and breezed through a mistake-free routine for a score of 14.366, which moved her into gold and guaranteed her a medal, prompting roars of applause from the crowd.

The clouds had parted for Biles to win an eighth Olympic gold and first ever on the beam, but she walked backward and off the beam after a back handspring-layout stepout-layout stepout, a sequence she’s rarely erred on historically. Biles climbed back on and stuck her dismount then, after an interminable wait, she was given a score of 13.100, the same as Lee and out of the medals.

Earlier, China’s Zou Jingyuan won the gold in the men’s gymnastics parallel bars event, becoming the first man in 32 years to win medals on rings and bars at the same Olympics. Ukraine’s Illia Kovtun won the silver medal and Japan’s Shinnosuke Oka took the bronze. In the men’s horizontal bar final, Oka won his third gold medal of the Olympics in a final riddled with mistakes. Colombian teenager Angel Barajas took silver and Taiwan’s Tang Chia-hung and China’s Zhang Boheng shared bronze.

• This article was amended on 6 August 2024 to correct the beam scores given to Alice D’Amato and Simone Biles. Also, Italy’s gold medal for the team event was its first team, not individual, gymnastics medal for 96 years.