MELBOURNE, Australia — After Jessica Pegula earned her first trip to a Grand Slam quarterfinal, the daughter of the owners of Buffalo’s NFL and NHL franchises scribbled on the screen of an Australian Open courtside TV camera: “hi mom, hi dad, see you next rd Jen B.”

In addition to a shoutout to her parents, that was a message for Jennifer Brady, a good pal of Pegula’s whose fourth-round match was up next in Rod Laver Arena today.

And after Brady won, too, setting up an all-American matchup against Pegula with a berth in the final four at stake, she used a blue marker to respond in kind, writing: “Bring it Jess!”

“It’s an opportunity for both of us,” Pegula said, recalling that she and Brady became close after playing doubles together for the United States in the team competition now known as the Billie Jean King Cup. “I’m just happy I’m here; she’s been playing some good tennis, solidifying herself as a top player.”

The 61st-ranked Pegula beat No. 5 seed Elina Svitolina of Ukraine 6-4, 3-6, 6-3, before the 22nd-seeded Brady, a Pennsylvanian who played college tennis at UCLA, had a 6-1, 7-5 victory over No. 28 Donna Vekic of Croatia.

Brady was one of the 72 players who had to go through a hard lockdown — two weeks stuck in a hotel room, not allowed to leave for any reason — after flying to Australia in January because someone on their flight tested positive for COVID-19 upon arrival.

Brady and Pegula gave the U.S. at least three women’s quarterfinalists at Melbourne Park, joining 23-time Grand Slam champion Serena Williams, who advanced a day earlier. And a fourth was a possibility, too, because unseeded Shelby Rogers played No. 1 Ash Barty for another spot in the round of eight.

The other remaining women’s match was No. 18 Elise Mertens vs. Karolina Muchova.

“I mean, it’s pretty awesome to see. I hope we can all push through,” Pegula said. “The last, I don’t know, year or so, we’ve really all pushed each other. Maybe we haven’t said it to each other, but I think we all can feel it.”

She is on quite a breakthrough run.

Pegula has won four matches at Melbourne Park over the past week — including victories over two-time Australian Open champion Victoria Azarenka and 2011 U.S. Open champion Sam Stosur — after entering the hard-court tournament with a total of three wins at majors for her career.

Also significant for Pegula, who works with Venus Williams’ former coach, David Witt: She came into the day with an 0-6 record against Top 10 women.

Witt said Pegula’s rising confidence is a big part of her progress. She found a sort of kinship with her family’s football team, the Bills, who made the playoffs three of the past four seasons behind quarterback Josh Allen after going nearly two decades without a trip to the postseason.

“Even last year, when he wasn’t playing that well, I was like, ‘I like this kid.’ I loved his competitive spirit. He was a gamer. He just wanted to win. That’s something you love to see,” she said about Allen. “It’s definitely something I think I tried to take into my game, even watching the team getting that grit, that competitive attitude, having that mindset — in tennis, it’s like 90 percent, sometimes, of the matches. It’s been really cool to watch them and kind of channel that energy into how I’ve been doing.”

Brady’s progress is far less surprising, given that she made it to the semifinals at the U.S. Open in September before losing to eventual champion Naomi Osaka.

Vekic’s right knee was heavily taped by a trainer early in the second set, which eventually got to 5-all. But Brady broke at love there when Vekic double-faulted, then held for the victory.

There will be a one-nation men’s quarterfinal, too, between Russians Daniil Medvedev vs. Andrey Rublev. Medvedev, the 2019 U.S. Open runner-up, eliminated 192nd-ranked American Mackenzie McDonald 6-4, 6-2, 6-3 in 1 1/2 hours, while Rublev moved on when No. 22 Casper Ruud stopped because of an injury after dropping the first two sets.

A third Russian man, 114th-ranked qualifier Aslan Karatsev, already had advanced, giving the country a trio of quarterfinalists at a major tournament for the only time in the professional era.

Also on that half of the draw, Rafael Nadal moved closer to a men’s-record 21st Grand Slam trophy by overwhelming No. 16 Fabio Fognini 6-3, 6-4, 6-2. Nadal’s next opponent will be No. 5 Stefanos Tsitsipas or No. 9 Matteo Berrettini.

With the sky blue and the temperature in the low 70s Fahrenheit (low 20s Celsius), and no fans in the stands for the third day in a row because of a local COVID-19 lockdown, Pegula dictated groundstroke exchanges from right along the baseline.

In the early going, she pushed around two-time Grand Slam semifinalist Svitolina, who eliminated American teenager Coco Gauff in the second round, and went up by a set and a break at 1-0 in the second.

Up until then, Pegula had not been broken.

But that’s where Svitolina, everything slipping away, made a stand. She suddenly broke Pegula twice in a row, part of a four-game run that put Svitolina ahead 4-1 in the second set on the way to forcing a third.

As if flipping a switch, or remembering what worked so well earlier, Pegula returned to her more aggressive brand of hit-to-the-corners play and led 4-1. She did get broken to 4-3, but broke right back, then served out the most important victory of her career by grabbing the last four points after falling behind love-30.

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