MELBOURNE, Australia -- Thursday is Australia Day, the celebration marking the date British sovereignty arrived here in 1788.

At the Australian Open, it will be a star-spangled day for America, with three U.S. women playing in the semifinals.

No. 2-seeded Serena Williams will play unseeded (and unlikely) Mirjana Lucic-Baroni of Croatia, and No. 13 Venus Williams will meet unseeded Coco Vandeweghe.

Serena hasn't played Lucic-Baroni this century, but she won both of their matches in the late 1990s. More recently, Venus defeated Vandeweghe in their only meeting last year in Rome.

Serena booked her spot with a powerful and convincing 6-2, 6-3 win over No. 9 seed Johanna Konta of Great Britain. It was over in 75 minutes, and it secured the 10th consecutive major semifinal appearance for Serena, a remarkable achievement of high-level consistency.

With two more match wins in Melbourne, Serena will regain her No. 1 ranking.

Earlier, Lucic-Baroni surprised No. 5 seed Karolina Pliskova 6-4, 3-6, 6-4 more than 17 years after she reached her first Grand Slam semifinal, as a 17-year-old at Wimbledon in 1999. Lucic-Baroni is, however, troubled by an injured left thigh.

This is only the fourth time in Open-era history, dating back to 1968, that three semifinalists have been over 30 years old. Venus, 36, is trying to become the oldest woman to win a Grand Slam singles title. Serena, who is 35 and already holds that distinction, will try to beat the 34-year-old Lucic-Baroni.

At times, Serena struggled with her first serve; she landed only 45 percent of them in but managed to win 88 percent of those points when she did.

She finished with a flourish, though, delivering three unreturnable serves in the final game -- two of them aces -- and ultimately winning at love.

"I was just really happy to get through that," Serena said in her on-court interview. "The main focus is actually my serve. I missed a lot today and got frustrated. I thought, 'Stop complaining, don't be Babyrena.' Just have fun and really try to enjoy the moment,' and I did.

Serena Williams remained on track for an Open-era record 23rd Grand Slam title after beating ninth-seeded Johanna Konta 6-2, 6-3 in the Australian Open quarterfinals on Wednesday. Quinn Rooney/Getty Images

Serena acknowledged in her postmatch news conference that her first serve "hasn't been great all tournament, so I've been kind of relying on my second serve."

"Also, my whole game," she added. "I've been relying on my groundstrokes, forehand, backhand. My returns have really picked up."

Konta, the recent Sydney champion who came in on an 18-set winning streak, simply wasn't ready for the weight of shots coming from Serena.

Fourteen years ago to the day, Serena beat Venus in the final here to complete the Serena Slam. On Saturday, there's a decent chance they could renew that sibling rivalry in the final.

"Thirty is the new 10," Serena said. "I'm so proud of Mirjana. It's so good to see her back out here in the semifinals. No matter what happens, somebody older than 34 is going to be in the final."

Lucic-Baroni's earlier win was far more emotional.

When she won, she crossed herself several times and fell to her knees, tears in her eyes.

"I can't believe I'm in semifinals again," Lucic-Baroni said in her on-court interview. "I feel a little bit in shock right now. I never could dream about being here again."

And then words failed her and she began crying again.

Ranked No. 79 in the world and nursing a left thigh injury, Mirjana Lucic-Baroni, 34, defeated US Open finalist and fifth-seeded Karolina Pliskova in three sets at the Australian Open to reach her first Grand Slam semifinal since Wimbledon in 1999. Clive Brunskill/Getty Images

In truth, Pliskova -- who is a decade and 12 days younger than Lucic-Baroni -- gave this one away. While Lucic-Baroni exited the court for an injury timeout, Pliskova was left to contemplate her 4-3 third-set advantage. Lucic-Baroni held serve, then broke Pliskova, who hammered a backhand and a forehand well out. Lucic-Baroni held serve to close out the victory, winning 12 of the last 13 points after taking that six-minute timeout.

Pliskova, who was 9-0 in 2017, surprised Serena in the 2016 US Open semifinals, before losing to Angelique Kerber in the final.

Lucic-Baroni was seen as an emerging professional star when she won the 1996 US Open junior title and repeated at the 1997 Australian Open. She was only the third player in Open era history to win two junior Slams by the age of 14, joining Martina Hingis and Jennifer Capriati. At 15, she won her first WTA-level title, the fifth-youngest winner ever.

But Lucic-Baroni didn't play a Grand Slam event from 2003 to 2009 due to injuries, personal setbacks and financial issues. If she hadn't been a tennis player, she said she would have been an archaeologist.

Lucic-Baroni had enjoyed a resurgence, reaching the fourth round of the 2014 US Open, but no one was prepared for this.

She previously had lost eight of nine matches at the Australian Open, but Lucic-Baroni has won all five matches here this year.

"To me, this is overwhelming," she said. "I will never, ever, ever forget this day. This has made everything bad in my life OK."

Serena said that witnessing Lucic-Baroni never give up "is super inspiring to me. It's a wonderful story."

"At the end of the day," Serena added, "it really helps me to realize that you have to always go for your dreams. So I feel like it's just great."