Austria also qualified with a dramatic 3-2 win over Hungary, while Belgium and Denmark took commanding 2-0 leads over Australia and Spain.
After Germany took a 2-0 lead on Friday in Tokyo, their victory was completed when Kevin Krawietz and Tim Puetz saved three set points in the second set to beat Japan's Yosuke Watanuki and Takeru Yuzuki 6-3, 7-6(4) in the doubles. Justin Engel then beat Rei Sakamoto 6-3, 6-7(2), 10-7.
Last year's semi-finalists Germany, are the first team to enter the Final 8 through the qualifiers, joining hosts Italy in the culminating round set for November in Bologna.
"Right now, the locker room is dancing and singing. We’re looking forward to Bologna and hopefully we’re getting one step further," Germany captain Michael Kohlmann said.
Argentina also qualified when Andres Molteni and Horacio Zeballos beat the Dutch duo of Sander Arends and Botic van de Zandschulp 6-3, 7-5 to take an unassailable 3-0 lead in Groningen.
Hungary, who had lost both their matches to Austria on Friday, fought back with back-to-back wins in Debrecen.
Fabian Marozsan and Zsombor Piros edged the Austrian pair of Alexander Erler and Lucas Miedler 7-6(4) 7-6(2) before Piros beat Lukas Neumayer in a singles match to bring Hungary level at 2-2.
But Austria won the tie in the fifth match, with Jurij Rodionov earning a dominant 6-2, 6-1 victory over Marton Fucsovics.
France also secured their place in the Final 8 as Corentin Moutet beat Marin Cilic, securing a 3-1 victory over Croatia in Osijek.
Last year's quarter-finalists Spain are on the verge of elimination as Denmark took a 2-0 lead over them in Marbella, with world number 11 Holger Rune beating Pablo Carreno Busta and Elmer Moller defeating Jaume Munar.
Collignon sees off De Minaur
Australia's Alex de Minaur, who reached the US Open quarter-finals earlier this month, lost to Belgium's Raphael Collignon 7-5, 3-6, 6-3 in Sydney, and Zizou Bergs fought through cramps to beat Jordan Thompson in straight sets to consolidate the visitors' 2-0 lead.
"I think when you play for your country, there is no pain," Bergs said.
Australia captain Lleyton Hewitt said the hosts needed to stay positive as they could still stage a comeback to win the tie on Sunday.
"There's nothing better than a good comeback story. We're a long way from being done and we can just easily turn this thing around," De Minaur said.