Victory for Italy's Simone Bolelli and Fabio Fognini over Japan's Ben McLachlan and Yasutaka Uchiyama in Morioka gave the Italians a 2-1 lead while in the final World Group tie Hungary's Marton Fucsovics and Attila Balazs held off Belgium's Joris de Loore and Ruben Bemelmans to win 6-3, 6-4, 6-7 (2-7), 4-6, 7-5 in Liege and cut the hosts lead to 2-1.
The final reverse singles rubber set to feature Australian No.2 Alex de Minaur against Jan-Lennard Struff was abandoned after Germany sealed the win. "It's awesome, it's an unbelievable feeling", Zverev said on court after steering Germany to the quarter-finals for the first time in three years.
World No 14 Kyrgios - ranked 44 places higher than his opponent - seemed to hardly break a sweat as he overpowered the German No 2 6-4 6-4 6-4.
The sight of John Millman practising with the Australian team fuelled speculation that rookie teenager Alex de Minaur may miss what looms as a crunch Davis Cup singles rubber against Germany in Brisbane on Sunday.
"He's in their team for a reason - they're a world class team and we know to expect the best from them", Ebden said. "We showed we have a lot of good players, a lot of strong players".
"It's tough not to put in your best performance".
Kyrgios's frustrations at an elbow injury boiled over when he smashed a racquet and received a point penalty in the second set against Zverev.
The hot-headed Aussie lost his cool in the 6-2 7-6 6-2 loss to Germany's Alex Zverev.
Kyrgios appeared to be struggling with a right elbow ailment, taking a time-out for treatment while leading 4-3 in the second set. "I mean, I thought he played great today - but my serve was not really there and that affects the rest of my game".
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Australia team captain Lleyton Hewitt said the injury - not the must win situation - had made it hard for Kyrgios to focus.
"It's obviously frustrating. Two of those five-set losses could have gone either way (but) that's tennis", Hewitt said.
The United States surged to an unbeatable 3-0 lead to eliminate 2010 champions Serbia in the first round of the Davis Cup Saturday.
Australia will contest September's World Group playoffs.
Joining Serbia at the exit was 2014 victor Switzerland, which was also overwhelmed 3-0 by Kazakhstan after failing to mount much of a challenge in the absence of 20-time grand slam champion Roger Federer.
Kyrgios - who had won six of his past seven rubbers - now has a 9-6 Cup singles record while Zverev improved his tally to 3-4.
He also made the semi-finals of the Australian Open in doubles last month.