Serena Williams and Simona Halep started the season with straight-sets victories in Melbourne a week before the Australian Open gets under way.
Williams and Halep played in an exhibition event with a crowd of 4,000 watching on in Adelaide last Friday and they were back in competitive action three days later.
Legendary American Williams beat Daria Gavrilova 6-1 6-4 to move into the third round of the Yarra Valley Classic.
The fifth seed struck 27 winners to 15 unforced errors on Margaret Court Arena as she set up a meeting with Tsvetana Pironkova, who ousted Donna Vekic 1-6 6-4 6-2.
Williams said: "It was a good match for me. It wasn't easy at all. It was lots of rallies and lots of movement, and she's from here, so she obviously always plays hard. So it was really good and it felt good to clinch that in the end."
Third seed Karolina Pliskova, Petra Martic, Danielle Collins and Marketa Vondrousova also advanced to the last 16 on Monday.
Elsewhere, top seed Halep is through to the third round of the Gippsland Trophy following a 6-4 6-4 win over Anastasia Potapova.
Halep hit 23 winners and broke twice in each set in what was her first official match since October.
Elina Svitolina, the third seed, beat Andrea Petkovic 6-1 6-4, while Coco Gauff, Ekaterina Alexandrova and Jelena Ostapenko were among the other winners seven days prior to the start of the first grand slam of 2021.
Reigning champion Sabalenka pushed by Linette at Madrid Open
Aryna Sabalenka got her Madrid Open campaign started with a 6-4 3-6 6-3 win over Magda Linette on Friday.
Sabalenka could not quite hit her peak form against Linette, but the world number two nevertheless got the job done after going the distance.
The Belarusian is hunting a record-equalling third title in Madrid, where she is the reigning champion, though she has not won back-to-back matches at a tournament since winning the Australian Open.
"It's not about being confident," Sabalenka said. "It's about how much you're ready to do to get it. It's about the hard work and to be ready, be ready for the big fights. I feel like confidence is not going to help you in those big matches. It's about staying there and fighting for it."
Data Debrief
Sabalenka (70 per cent, 56-24) is now one of five active players since 2020 to hold a winning percentage of 70 per cent or higher at WTA-1000 events.
Iga Swiatek, Simona Halep, Elena Rybakina and Jessica Pegula are the other players to feature on that list.
Rybakina continues clay winning streak with victory over Bronzetti
In-form Elena Rybakina has moved into the last 32 of the Madrid Open after a straight sets victory over Italian Lucia Bronzetti.
Number four seed Rybakina triumphed 6-4 6-3 on Friday and will next face either Marta Kostyuk or Mayar Sherif.
Rybakina was broken early in each set but ultimately had few problems getting over the line, converting four of her five break points to continue an impressive run of results after winning the Stuttgart Open last week.
She has now won five consecutive WTA matches and has 13 straight wins on clay courts to her name in a superb streak that started one year ago.
Data Debrief: Rybakina in elite company
Since the start of 2020, only two other players have claimed as many 13 consecutive WTA wins on clay, and they are Iga Swiatek and Simona Halep, so Rybakina is in elite company.
Rybakina's last defeat on this surface came in the 2023 edition of the Madrid Open, when she fell to Anna Kalinskaya in her first match, so this win represented a better start to her campaign in the Spanish capital.
World number one Swiatek sees off Xiyu in Madrid opener
World number one Iga Swiatek overcame Wang Xiyu with the minimum of fuss on Thursday to progress to the third round of the Madrid Open.
Swiatek has yet to win the title in Madrid, which is the only clay-court European event at which the Pole has not triumphed, but she got off to a flying start with a 6-1 6-4 victory over Xiyu.
"I love this place. I got to know the city a little better last year," Swiatek said. "So this time I feel more comfortable around."
Next up for the 22-year-old is a third-round tie against 27th seed Sorana Cirstea on Saturday.
Data Debrief
Swiatek has registered 150 match wins on the WTA Tour since the start of 2022. Elena Rybakina and Coco Gauff are the next best with 108 wins each.
She also became the first player born this century to claim 50 combined match wins in Madrid, Rome and Roland-Garros, since the inaugural women's singles event at the Madrid Open in 2009.
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