The tournament hosts were staring down the barrel of elimination from the $17 million teams' showpiece after an off-colour Maya Joint suffered a 6-4 6-1 loss to dual grand slam champion Barbora Krejcikova in Tuesday night's opening singles match.
But de Minaur stepped up to level the must-win clash with Czechia with a 6-4 6-1 triumph over boom talent Jakub Mensik, the youngest player in the world's top 20.
Australia's tennis 'Demon' then delivered again after skipper Lleyton Hewitt asked his spearhead to replace John-Patrick Smith and partner Storm Hunter in the deciding mixed doubles.
De Minaur and Hunter duly denied Dalibor Svrcina and Miram Skoch 6-2 6-3 in a tense encounter that belied the lopsided scoreline to secure Australia a 2-1 victory and Group D honours.
The reward for the 2024 semi-finalists is a likely quarter-final showdown on Friday night at Ken Rosewall Arena with Iga Swiatek's Team Poland, while Czechia also progressed to the last eight as the best runners-up from the three Sydney pools.
While Joint misfired on her return after missing Australia's weekend win over Norway through illness, de Minaur dazzled in rebounding from his season-opening loss to Casper Ruud and improving his perfect record over the 18th-ranked Mensik to five from five.
"Obviously I didn't start the year the way I wanted to but I tried to not take that match too much into account," de Minaur said.
"I thought Casper played really well but something that I've done really well in my career is bouncing back, so I'm very happy with the way I bounced back today."
De Minaur's triumph, coupled with a shock loss earlier on Tuesday for Felix Auger-Aliassime in Canada's elimination from the event, also vaulted the 26-year-old to a career-high No.5 in the live ATP rankings.
If he maintains that position when the new rankings are released on Monday, de Minaur will enter the Australian Open seeded fifth, behind only heavyweights Carlos Alcaraz, two-time defending AO champ Jannik Sinner, Alexander Zverev and 10-time winner Novak Djokovic.Â
On track to gain a first-time grand slam seeding at this month's Australian Open, Joint soared to No.32 in the world in a spectacular two-title season in 2025.
But facing Krejcikova - the 2021 French Open winner and 2024 Wimbledon champion - proved too tall an order for the underdone 19-year-old in her first match of the year.
The accomplished Krejcikova, who also boasts a rare career golden slam in doubles, broke Joint in the opening games of both sets to have the home favourite on the back foot throughout.
While de Minaur captured the headlines for his high-pressure double act, Hewitt also once again has Hunter to thank for Australia reaching the quarter-finals for a second time in the past three years.
As well as her successful support role on Tuesday night, the resurgent 31-year-old played the hero in Saturday's victory over Norway, winning her singles match after deputising for Joint and then combining with Smith to clinch the tie with a thrilling doubles comeback display.
"I definitely knew this match was a must win and, yeah, pressure is a privilege and to do it at home - we had the crowd, home advantage and we weren't going to lose this one," Hunter said.
"Demon brings energy. He's clutch under pressure, so I felt really confident with him by my side."
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