World No.9 de Minaur put on a devastating display in his first hit-out of the season at Sydney's Ken Rosewall Arena, posting a 6-1 6-4 result over Tomas Etcheverry in 75 minutes.
His win squared the tie after Nadia Podoroska beat Olivia Gadecki 6-2 6-4 in Saturday's women's singles earlier on Saturday.
Olympic doubles gold medallist Matthew Ebden and Ellen Perez had to finish off the job in the mixed doubles against Etcheverry and Maria Carle - who came in for Podoroska - but lost 6-2 6-4.
Australia, captained by Lleyton Hewitt, endured a similar fate last year, losing 2-1 to Great Britain in the first round of group stages, but were able to scrape their way to the quarter-finals.
Hewitt's team returns to action on New Year's day when they face a Great Britain outfit including Billy Harris and de Minaur's fiancee Katie Boulter.
All smiles from Lleyton Hewitt 😃🇦🇺— United Cup (@UnitedCupTennis) @alexdeminaur is going deep into his bag of tricks at the #UnitedCup pic.twitter.com/fEFnGdJArlDecember 28, 2024
In his singles match, Sydney local de Minaur claimed the first set against Etcheverry within 28 minutes and sent the near-capacity crowd rocking with every point earned.
Etcheverry took four hard-earned games in the second set after finding his rhythm, but de Minaur prevailed with great precision.
"Thank God I executed today and got the win for Australia," de Minaur said.
"Just being back here in Sydney, I love it here.
"I just told myself to back myself and play the type of tennis I wanted to play."
Olivia Gadecki getting the Aussie crowd on their feet 🇦🇺— United Cup (@UnitedCupTennis) #UnitedCup pic.twitter.com/7y4yg9Fwc9December 28, 2024
In the women's singles, emerging star Gadecki battled nerves and was broken in her opening game, before losing the first set.
Cheered on by a boisterous home crowd in the second, the 22-year-old looked ready to mount a comeback after launching ahead 4-3 but was ultimately undone by her errors in the 88-minute contest.
The scoreline was the same as when Gadecki last met Podoroska at this year's Indian Wells Open.
"It's never easy, the first match back but I'm happy with how I played and how I competed," Gadecki said.
"Hopefully with every match, it will get better and better."
Gadecki is the nation's only woman to gain direct entry to the Australian Open, having reached the world's top 100 with a career-best run to the Guadalajara Open final in September.
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