The 32-times winners were without big names like US Open runner-up Taylor Fritz, Tommy Paul and Frances Tiafoe for their Finals group stage campaign this week but still had plenty of firepower to down Germany and complete a third straight win.
Brandon Nakashima gave the Americans an unassailable 2-0 lead by comfortably beating Maximilian Marterer 6-4 6-2 in the second singles match of the day to stay perfect in his debut Davis Cup campaign.
"It's been unbelievable this whole week. It's special to be part of this team," said Nakashima.
"To represent the country has always been a dream of mine since I started playing tennis, so I'm super happy that I was able to get three wins on the board for the team."
World number 309 Reilly Opelka, back on the circuit this season after hip and wrist surgeries, saved three matchpoints and cranked up his big serve when it mattered to outlast debutant Henri Squire 6-7(4) 7-6(9) 6-3 7(4) 7-6(9) 6-3 earlier.
Tim Puetz and Kevin Krawietz overcame Rajeev Ram and Austin Krajicek 6-1 7-6(4) in the doubles clash later but US captain Bob Bryan was satisfied with a splendid week that highlighted the team's singles depth.
"We've got a lot of great players in the U.S. right now, you can see it in the rankings. A lot of guys to choose from for the Finals," Bryan said.
"Hats off to these guys for coming here and carrying us to Malaga. We've got a couple of months to relax and get ready but it's going to be fun over there.
"We're looking forward to it."
The top two countries from four groups based in different cities will go through to the Final 8 knockout stage to be held in Malaga in November.
Heavyweights Spain and Australia had also qualified after Friday's action along with the United States and Germany.
They were joined by defending champions Italy, who advanced after Brazil took a 2-0 lead against Belgium in Bologna as Joao Fonseca beat Raphael Collignon 6-3 6-7(2) 6-3 before Thiago Monteiro edged out Zizou Bergs 4-6 7-6(5) 7-5.
Belgium kept alive their own hopes of going through from Group A as Sander Gille and Joran Vliegen sealed a 6-3 3-6 6-4 win over Rafael Matos and Felipe Meligeni Alves.
Argentina earned their first quarter-final appearance since 2019 with a 3-0 win over Finland in Group D in Manchester, after Maximo Gonzalez and Andres Molteni moved past Harri Heliovaara and Patrick Kaukovalta 6-3(7) 6-4 6-3.
Tomas Martin Etcheverry earlier beat Eero Vasa 7-6(5) 6-3 and Francisco Cerundolo saw off Otto Virtanen 6-7(4) 6-1 6-0.
France won a doubles decider against Czech Republic late on Saturday evening in Group B although neither are in the hunt after losing both their matches in Valencia.
