In Tatabanya, Hungary, Christian Harrison, the Australian Open doubles champion, paired with Austin Krajicek to claim the clinching point for record 32-time winners the US with a 6-4, 3-6, 6-3 victory over Fabian Marozsan and Zsombor Piros.
Harrison, making his Davis Cup debut, said: "I had such a good time this week, I already forgot about" the Australian Open, as the Americans won 4-0.
The United States will travel to Czech Republic for a place in the Final 8.
France progressed 3-1 at home to Slovakia after Arthur Rinderknech sealed the vital victory 7-5, 7-6 (6) against Alex Molcan in the second match of the day following Benjamin Bonzi and Pierre-Hugues Herbert's doubles win.
"It was a great doubles match," Rinderknech said.
"They played very well. It allowed me to go onto the court with a lot of confidence. I needed it because Molcan was really strong today."
France's next tie will be a trip across the Atlantic Ocean to Canada.
In Quito, Ecuador seized an unassailable lead against Australia as Gonzalo Escobar and Diego Hidalgo beat Rinky Hijikata and Jordan Thompson 7-6 (5), 6-4 to put the hosts 3-0 ahead.
Ecuador will seek to continue their giant-killing exploits in the next round away to Great Britain.
Despite missing world number six Alex De Minaur, Australia still seemed to have enough on paper to win the tie with top 100-ranked James Duckworth and 2024 US Open men's doubles champion Thompson.
After Alvaro Guillen Meza had beaten Hijikata in three sets though, world number 257 Andres Andrade defeated Duckworth 3-6, 6-3, 7-5 to tee up the upset on clay.
Roared on by their fans in Busan, South Korea came from behind to beat Argentina 3-2.
After Argentina took the lead with a doubles victory, Kwon Soon-woo - ranked 248 spots lower than his opponent - beat Thiago Agustin Tirante in three sets to force a decider, which Chung Hyeon duly won.
The Koreans will next play India, who edged the Netherlands 3-2 in Bengaluru as 465th-ranked Dhakshineswar Suresh bested world number 162 Guy Den Ouden 6-4, 7-6 (4) in the decider.
In Plovdiv, Belgium swept aside hosts Bulgaria 4-0 to set up a meeting with Austria.
The Czechs meanwhile beat visiting Sweden 3-1, with Petr Nouza and Patrik Rikl's opening doubles win enough to ensure their country's progression.
Germany, Austria, Chile, Croatia, Britain and Canada had locked up round two qualifying places earlier in the weekend.