With a clean routine devoid of any major errors, D'Amato earned 14.366 points, enough to win her gold.
Zhou Yaqin of China made a solid start to her routine but she had to bend over and grab the beam with both hands during her jump sequence to prevent herself from falling. Despite the error, she clinched silver with 14.100 points.
D'Amato's compatriot Manila Esposito finished third, 0.1 of a point behind her Chinese rival.
Biles, the most decorated gymnast of all time, was one of four finalists to fall off the apparatus on Monday.
The American, a two-time Olympic bronze medallist and a four-time world champion on the balance beam, finished a disappointing fifth with 13.100.
The 27-year-old was had been expected to perform a sequence featuring handspring layout-layout but and she aborted the series after the first layout and loud gasps could be heard around Bercy Arena as she lost her balance and slipped off.
Biles' teammate Sunisa Lee, the 2020 all around Olympic champion, crashed to the mat during her flight sequence and finished sixth.
"It was just crazy to kind of see how everybody was going down like that," Lee said. "But I think it's just because there's just so much pressure. You could feel the tension in the room."
Lee said the absence of music in the background during the balance beam final and an eerily quiet crowd who was shushing attempts to cheer had unnerved some gymnasts
"Me and Simone were like, 'why are they shushing? Like we're just trying to cheer," Lee said.
