Playing his first match since Wimbledon seven weeks ago, de Minaur fired up when it mattered to eke out a 6-3 6-4 5-7 6-4 victory over gritty American Marcos Giron and give Australia at least nine players in the second round.
Thanasi Kokkinakis, Jordan Thompson and inspired wildcard Tristan Skoolkate also scored rousing wins to continue Australia's magnificent start to the final grand slam of the year.
Fan favourite Kokkinakis roared with emotion and received a standing ovation on The Grandstand after upsetting dual grand slam runner-up Stefanos Tsitsipas 7-6 (7-5) 4-6 6-3 7-5 for the biggest grand slam win of his stop-start career.
Thanasi Kokkinakis couldn't contain his excitement after beating Stefanos Tsitsipas. (EPA PHOTO)
Incredibly, the fighting four-set triumph over the 11th seed was only Kokkinakis's second victory at the Open in nine injury-plagued years.
"A massive relief," he said.
"Super happy, super pumped. It's been well documented I've had some tight ones, but I'm starting to get on the winning side of them now."
The 28-year-old's reward is a golden opportunity to finally make a grand slam run in a wide open pocket of the draw.
Kokkinakis next faces unseeded Nuno Borges, with Schoolkate a potential round-three opponent following the West Australian's own watershed win over Taro Daniel.
Schoolkate vindicated his wildcard entry with a steely 4-6 4-6 6-4 7-6 (8-6) 6-4 comeback victory on his long-awaited grand slam main-draw debut.
Australia's Tristan Schoolkate fought back from two sets down to beat Taro Daniel. (AP PHOTO)
"It's fantastic. I'm obviously very happy to get through that match," said the world No.193.
"Especially being down two sets to love, it seems like a long way back.
"But I thought if I just kept with it and keep myself in the match, there's no time limit in tennis.
"As long as you're still playing, you've still got a chance."
The 23-year-old Schoolkate earned a second-round shot at Czeck Jakub Mensik, not to mention a life-changing career pay day of at least $US140,000 ($207,000).Â
Thompson earlier shook off the disappointment of missing a seeding by one lousy rankings spot to blow away Constant Lestienne 6-1 6-3 6-2 in less than two hours.
The world No.32 did his best to escape the searing heat by breaking the Frenchman six times without dropping his own serve once.
Thompson will play world No.7 Hubert Hurkacz for a place in the last 32.
De Minaur's next test will come against Finnish qualifier Otto Virtanen on Thursday (Friday AEST) after he had to dig deep to avoid being pushed to a fifth set against Giron.
But having been forced to pull out of his Wimbledon quarter-final against Novak Djokovic with a hip injury, and then from a second straight Olympic Games, the world No.10 will be hugely relieved to be back in grand slam contention in New York.
Max Purcell was Australia's ninth player to progress after ousting his Sydney mate Aleksandar Vukic 7-5 6-4 6-3.
Alexei Popyrin, Rinky Hijikata, Ajla Tomljanovic and 18-year-old qualifier Maya Joint all won on day one.
But women's wildcard Taylah Preston's international grand slam debut lasted just 61 minutes in a 6-2 6-0 first-round loss to Russian seed Anastasia Pavlyuchenkova.
Daria Saville's comeback from a foot injury ended in frustration and despair, the Australian No.1 losing 6-3 4-6 7-6 (10-6) to Japanese qualifier Ena Shibahara in a three-hour, 16-minute cliffhanger.
And Destanee Aiava's run from qualifying ended with a gallant 6-1 7-6 (7-1) loss to fourth seed Elena Rybakina after the Australian had three set points to take the match against the 2022 Wimbledon champion to a decider.
A whopping 13 Australians were scheduled to play on Tuesday, with men's qualifier Li Tu preparing for a dream date with reigning French Open and Wimbledon champion Carlos Alcaraz in the men's feature night match on Arthur Ashe Stadium.
Chris O'Connell faces 26th seed Nicolas Jarry, while James Duckworth and Arina Rodionova are also in later action.
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