She scored 14,000 for her routine in Tuesday’s final, initially finishing second behind China’s Tang Xijing at 14,233.
However, 16-year-old Guan, the best qualifier in the event and the last to perform her routine, took the gold medal position with a score of 14.633.
Biles didn’t compete in four individual finals at the Tokyo Olympics — the all-around individual competition, the vault, the uneven bars and floor — but returned to a big round of applause from her American teammates sitting in a corner of the Ariake Gymnastics Center.
The bronze on the balance beam is her seventh Olympic medal and contributes to the team final silver she won last week. Biles, 24-year-old, also won bronze on the balance beam at the 2016 Rio Olympics.
For Guan, who cites Biles as her sports idol, and Tang, the gold and silver medals were their first at the Olympics.
“I never expected to get a medal,” Guan said. “My coach said, ‘This is your first time at the Olympics and nobody knows you, so just go in and do your best.’
“Actually I started gymnastics much later than other people so I think this is a good result for me. Although this competition is very tiring, I am very happy with this result.”
But Biles was all smiles after completing her ball routine in the final and waved enthusiastically to the crowd, some of whom responded with a standing ovation.
“It’s been a very long week, a very long five years. I didn’t expect to win a medal today, I just wanted to do it for myself, and that’s what I did,” Biles said.
“It certainly feels more special, this bronze, than the balance beam bronze at Rio. I will cherish it for a long time.”
Canada’s Ellie Black finished fourth with a score of 13,866, while Biles’ teammate Sunisa Lee, who won gold and bronze in the uneven bars last week, was fifth.
The balance beam was the last part of the Tokyo women’s artistic gymnastics program.