While Jessica Pegula and Madison Keys were leading the Americans to victory at the inaugural United Cup in Sydney, across the Tasman Sea, Coco Gauff was sprinting to the title in Auckland.

They all arrived in Melbourne oozing with the kind of confidence that only comes from winning and were joined by another United States player, Danielle Collins, who herself has thrived in the heat of the Australian summer.

All four are into Friday’s third round at Melbourne Park. Gauff is a perfect 7-0 this season, along with Keys (7-0), Pegula (6-1) and Collins (4-2) -- for a scalding combined start of 24-3 (.889). And then there’s Bernarda Pera, who knocked off rising Chinese star Zheng Qinwen, the No.29 seed, in the second round, making it five Americans among the top half’s 16 survivors.

Katie Volynets is lone American still alive in the bottom half.

Five things to know about American qualifier Katie Volynets

For Keys and Pegula, the United Cup team-building experience had, as an added bonus, ramifications for their individual games.

Australian Open: Gauff holds off Raducanu to reach third round

“I think I speak for everyone, it was truly the best two weeks of my whole life,” Keys told reporters. “To have the seven other amazing people and then all of our teams together, it was just a really great group of people. We still talk literally every single day. So I think just carrying that over outside of the event has been really great for all of us.”

Day 4 from the Australian Open

Keys, the No. 10-seeded American, might have the steepest challenge Friday, when she takes on No.24 Victoria Azarenka. The two-time Australian Open champion has won all three of the matches between them, most recently last year in Guadalajara. Keys won a second-set tiebreak, but fell in the third 6-1.

Her biggest focus this year is to minimize the damage when she’s not playing her best -- like that ultimate set against Azarenka. How does one do that, exactly?

“Try not to make dumb decisions mostly, which is still a work in progress,” Keys said, candidly. “But, I mean, for me it’s really just trying to let myself rely on making balls because I have become a much better mover, and I can stay in points, and I don’t necessarily have to be the aggressor all of the time.

“Even in matches where I start not playing amazing, figuring my way out, getting more comfortable and just giving myself the opportunity to get into matches. I think that’s what I’ve been the most proud of so far this season.”

No.13 Collins, too, will be tested by reigning Wimbledon champion and No. 22 seed Elena Rybakina. They’ve split the two matches they’ve played, with Collins winning in 2021 San Jose and Rybakina scoring a three-set victory to open the season in Adelaide. Collins, a finalist here a year ago, lost a surprising total of 31 games in her first two matches in Melbourne Park, the most for a third-rounder here in nine years.

“It’s going to be very tough because she’s playing aggressive, same as me, and she has very good serve,” Rybakina said after beating Kaja Juvan 6-2, 6-1. “So I have to be very focused on the return games and for sure on my service game.”

No.3 Pegula is up against unseeded Marta Kostyuk, a player she beat last year in Cincinnati in their only meeting.

Meanwhile, it’s an all-American match between No.7-ranked Gauff and No.41 Pera in a first-time match.

In beating Emma Raducanu in the last round, Gauff, 18, posted her 100th Hologic WTA Tour victory. She’s the first player to do that before the age of 19 since Caroline Wozniacki nearly14 years ago in Madrid. Gauff (100-51) doesn’t turn 19 until March 13.

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Pera, a 28-year-old left-hander, is coming off the best season of her career when she won her first two titles (Budapest and Hamburg) and cracked the Top 50 for the first time.

Here are three more notable second-round matches on the Friday schedule:

No.1 Iga Swiatek vs. Cristina Bucsa

It looked like the World No.1 might face the 2019 US Open champion, but Spain’s Busca, ranked No.100, won a rousing three-set match against Bianca Andreescu. Swiatek has won all four sets so far, against Jule Niemeier and Camila Osorio. These two have never met.

No.6 Maria Sakkari vs. Zhu Lin

Their only meeting was seven years ago in the third round of qualifying. Sakkari won to advance to her second career main draw at a Grand Slam. Sakkari needed three sets to get past qualifier Diana Shnaider. Zhu upset No.32 seed Jil Teichmann 6-2, 6-2. Zhu won two matches in Auckland, one of them against seven-time Grand Slam champion Venus Williams.

No.20 Barbora Krejcikova vs. Anhelina Kalinina

Krejcikova, the 2021 French Open champion, seems to be rounding back into form after a 2022 elbow injury. She’s won two straight-sets matches and holds a 1-0 head-to-head advantage over Kalinina. The No.39-ranked Ukraine player upset No.15 seed Petra Kvitova 7-5, 6-4.