Finland had the lead when Patrik Puistola quickly shot 2–1 in the middle of the second period.
But Puistola was involved even when the USA later in the period only needed 71 seconds to transform the deficit into a lead. Zeev Buium made it 2–2 on a rebound and then Puistola sat in the penalty box when Conor Garland fixed 3–2, his second goal in the match.
Shane Pinto added to 4–2 in the final period before team captain Clayton Keller sent in 5–2 into an empty net.
For the USA, hope lives on to reach the World Championship final for the first time since the gold in 1960.
Finland took its latest World Championship gold in 2022, but has since been knocked out in the quarterfinals three years in a row.
Switzerland, which won the group play in Danish Herning, had no problems beating Austria in Thursday's other early quarterfinal. The foundation for the 6–0 win was laid with three goals already in the first period.
It is likely that Switzerland will be Tre Kronor's semifinal opponent, if the Swedes manage to beat the Czech Republic at the Globen later in the evening.
