She scored 14.000 for her routine in Tuesday’s final, initially placing her second behind China’s Tang Xijing on 14.233.
However, the 16-year-old Guan, the top qualifier in the event and the last to perform her routine, moved into the gold medal position with a score of 14.633.
Biles did not compete in four individual finals at the Tokyo Olympics — the all-around individual competition, the vault, the uneven bars and floor — but returned to great applause from her USA teammates seated in one corner of the Ariake Gymnastics Centre.
The bronze in the balance beam is her seventh Olympic medal and adds to the team final silver she won last week. The 24-year-old Biles also won bronze in the balance beam at the 2016 Rio Olympics.
For Guan, who lists Biles as her sporting idol, and Tang, the gold and silver medals were their first at the Olympics.
More to follow