A battling Nick Kyrgios earned a morale-boosting victory over world number six Stefanos Tsitsipas on Tuesday, while Russia and Britain booked their spots in the ATP Cup quarter-finals.
Tsitsipas was on a roll after thrashing Alexander Zverev on Monday, but met his match in the temperamental Australian, who was on his best behaviour during the high-quality 7-6 (9/7), 6-7 (3/7), 7-6 (7/5) win.
"It was exhausting but a lot of fun. I knew it was going to be very tough... he's an amazing player and so young and is going to do some special things in this sport," said Kyrgios, who missed his last match with a sore back.
"I'm just glad we got the win. There was a lot of respect out there. He's a good player, a good kid."
Australia took the tie, with John Millman winning the other singles against Greece's Michail Pervolarakis 4-6, 6-1, 7-6 (7/1).
In contrast, Zverev cut a miserable figure after he meekly succumbed to another defeat, with the world number seven having some serious problems to iron out ahead of the Australian Open this month.
"Generally I'm not playing good, so there's a lot of things that I still need to improve, but it's the start of the season," said the German after crashing to Canada's Denis Shapovalov 6-2, 6-2.
"The first match (against Alex de Minaur) I actually thought I played okay -- the serving was horrible -- but then I played two very bad matches, but what can I do."
His poor form contributed to the Boris Becker-led Germany losing two of their three ties.
- 'Very special' -
Australia, along with Novak Djokovic's Serbia, had already qualified for the last eight in the 24-nation tournament as winners of their respective groups and they were joined by Russia, with Britain also sneaking in.
The British were on tenterhooks, with their fate in the hands of Belgium and Bulgaria after they beat Moldova 3-0.
Belgium ended up crushing the dreams of Grigor Dimitrov's Bulgaria in a deciding doubles clash and in doing so allowed Britain to win the group.
It was a cruel end for Dimitrov and his young team. They looked on track after Dimitar Kuzmanov thrashed Steve Darcis in the opening singles and Dimitrov took the first set in his showdown with David Goffin.
But Goffin bounced back to win with Sander Gille and Joran Vliegen clinching the doubles.
"Tough finding words right now. A very special feeling after pulling out the win today," said Vliegen after beating Dimitrov and Kuzmanov 3-6, 6-4, 10-7.
Britain put themselves in contention by thrashing Moldova, with Dan Evans crushing Radu Albot and Cameron Norrie easing past Alexander Cozbinov before Jamie Murray and Joe Salisbury won the doubles.
Rafael Nadal's Spain will also make the last eight if they beat Japan in Perth on Wednesday, as will the Marin Cilic-led Croatia by beating Argentina in Sydney.
The two best runners-up also go through and will be determined on the last day of round robin play Wednesday.
World number five Daniil Medvedev steered Russia to victory, ending Norwegian Casper Ruud's giant-killing run with a 6-3, 7-6 (8/6) win as the US Open finalist continued his ominous form.
"Against Casper I knew I had to finish some points at the net," he said. "I knew I had to be aggressive and I think it helped me a lot."
World number 17 Karen Khachanov easily beat Viktor Durasovic 6-2, 6-1 in the other singles before Russia made it 3-0 in the doubles.