Thompson is enjoying a career-best season at age 30, claiming his maiden ATP title in Mexico in February and being just one spot off a seeding in New York. He added to it with a steely 7-6 (7-2), 6-1, 7-5 defeat of the world No. 7.
"A good day at the office," Thompson said. "Down early in the first, he served for the first set, and he’s got one of the best serves on tour. So, to turn it around like I did was pretty impressive, even if I say so myself."
Wildcard Tristan Schoolkate went agonisingly close to joining them, going down 6-7 (4-7), 2-6, 6-2, 7-6 (7-5), 7-6 (10-3) to Jakub Mensik after having consecutive match points on the Czech's serve in the 10th game of the fourth set.
Thanasi Kokkinakis won't be among them after following his upset of Stefanos Tsitsipas with a 6-4, 7-5, 7-5 loss to Portugal's big-hitting world No. 34 Nuno Borges, who meets Mensik next. Max Purcell's campaign is also over, retiring abruptly while trailing American 14th seed Tommy Paul 7-5, 6-0, 1-0.
Australia has not had four men in the third round since the 1997 edition, when Patrick Rafter won the first of his back-to-back titles; Mark Philippoussis reached the fourth round; and Scott Draper and Mark Woodforde each made the round of 32.
Those results follow 20 Australians starting in the main draw across the men's and women's events - matching the most in 45 years - while the eight men who advanced to the second round equalled the country's 1976 effort. There are also a world-leading 10 Australian men inside the top 100.
O'Connell, who ousted Chilean 26th seed Nicolas Jarry in the first round, downed Italian qualifier Mattia Bellucci 6-3, 6-4, 3-6, 6-3 to book his berth, while de Minaur survived an early scare when trailing 5-2 to oust Finnish qualifier Otto Virtanen 7-5, 6-1, 7-6 (7-3).
Brit Dan Evans is de Minaur's third-round opponent.
Awaiting O'Connell, who shares Marinko Matosevic as his coach with Thompson, is world No. 1 and Australian Open champion Jannik Sinner in a rematch of their Miami Masters clash in March.
Virtanen's aggressive style initially rocked de Minaur, but the No. 10 seed gradually worked his way on top in typically dogged fashion, and the Finn also sought treatment for a lower-back problem in the second set.
"I'm obviously happy to be back on tour [after his hip injury at Wimbledon]," de Minaur said.
"Every day I'm getting a little bit better, and I'm looking forward to what's to come. Still not a lot of expectations, but I know every time I step out there; I'm going to compete, I'm going to try my hardest, and hopefully, put on a show, so let's see if I can keep it going."
Hurkacz's defeat means he has never advanced beyond the second round in seven trips to the US Open despite making the last 16 or better at every other slam.
The match swung wildly late in the first set after Hurkacz failed to serve it out, with Thompson - who will match his fourth-round run from the COVID-impacted 2020 event if he beats 30th-seeded Italian Matteo Arnaldi - producing a brilliant mix of defense, net-rushing and clutch hitting.
Thompson's Upset Victory
This was his fifth career top-10 scalp and second of the year - the other being German Alex Zverev en route to his Los Cabos title triumph - as well as his best victory at this level since a five-set success over Casper Ruud at Wimbledon three years ago.
Thompson has not been in the round of 32 at a slam since that same Wimbledon, but is well-positioned to be seeded at the Australian Open in January, which would greatly aid his chance of going deeper.
Hurkacz was projected to be de Minaur's fourth-round opponent, but that section is now wide open.
Thompson might instead be de Minaur's stumbling block as the latter tries to become the first Australian male since Lleyton Hewitt two decades ago to reach three consecutive major quarter-finals.
Hurkacz threatened to force his way back into the contest with break points in consecutive games late in the third set, but Thompson repeatedly delivered in the most important moments.
The pigeon-toed Pole's game unravelled after a strong start. Hurkacz committed only four unforced errors through the first nine games - when he led 5-4 with a break - but was up to 21 by the time he fell 4-0 behind in the second set, after dropping the opener in a tie-breaker.
A Commanding Performance
Thompson's stout defense, penchant for mixing up his shots and expert volleying played a significant part in building pressure on his opponent, but Hurkacz also made some inexplicable mistakes.
Thompson raced through the second set, but Hurkacz, whose frustration bubbled over several times, was a tougher proposition in the third.
The Australian fought back from 15-40 while trailing 4-3 - starting with a wonderfully executed serve-volley - then staved off another break point two games later, which doubled as a set point, with an inside-out forehand winner that followed another good first serve.
Thompson made fewer than half his first serves, but won 82 per cent of those points and hit 13 aces.
Hurkacz's missed opportunities came back to haunt him when his forehand landed wide off the net cord to fall into a 0-30 hole at five-all.
He dumped a backhand into the net on the next point then poorly dragged a forehand wide to drop serve again and effectively hand Thompson the match.
Thompson beat Rafael Nadal to make the Brisbane semi-finals in January and Taylor Fritz to reach the same stage at Queen's Club in June before advancing to the Atlanta final and Washington ATP 500 quarter-finals in the lead-up to the US Open. - with AAP
A Historic Moment for Australian Tennis
This incredible run by the Australian men is a testament to the depth and strength of the country's tennis program. It's a sign that the future of Australian tennis is looking bright, with a new generation of players ready to take on the world.
It's been a long time since Australia has seen such a successful start to the US Open by its men's players. The last time this happened was in 1997, when Patrick Rafter won his first US Open title and other players like Mark Philippoussis, Scott Draper, and Mark Woodforde also made it to the third round.
What's Next?
Thompson will now face the Italian Matteo Arnaldi in the third round. It's an opportunity for him to continue his impressive run and make history by reaching the fourth round of a Grand Slam for the second time.
The US Open is shaping up to be a memorable tournament for Australian tennis fans. With several of their players already making deep runs, there's plenty of excitement to come. Let's see if this historic run can continue for the Aussies.
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