Updated

Brisbane, Australia (SportsNetwork.com) - Serena Williams and Maria Sharapova were among the quarterfinal winners Thursday at the Brisbane International and will continue their rivalry in the semifinals of the Australian Open tune-up.

The top-seeded Williams cruised to a 6-3, 6-3, win over Slovakia's Dominika Cibulkova, while the third-seeded Sharapova rallied for a 4-6, 6-3, 6-2 victory over Estonia's Kaia Kanepi.

Williams and Sharapova are, arguably, the two biggest names in women's tennis and have met on 16 prior occasions. Williams has dominated the series with 14 wins, including 13 straight.

"I haven't had a lot of success against her in the past," said Sharapova after Thursday's win. "But it's the first tournament of the year. I came here wanting to play as many matches as I could and wanting to play the best. There's no substitute for getting ready for a Grand Slam than competing against the best. She's been on a roll the last couple of years with her level. I competed against her a few times last year; didn't work."

The two met four times in 2013 and Sharapova managed to take just one set against the top-ranked American. Three of those matches came in tournament finals -- Miami, Madrid and the French Open.

Sharapova hasn't beaten Williams since 2004, a 4-6, 6-2, 6-4 triumph in the final of the Tour Championships. The Russian also knocked off Williams earlier that year for the Wimbledon crown.

Kanepi, the 2012 Brisbane winner, tried her best to prevent the blockbuster matchup. She took the first set and went up a break in the second, but Sharapova battled back.

"She's a really tough opponent," Sharapova said of Kanepi. "She's won this tournament before, so I knew that she would be able to play on this court and she enjoys it. For me it was a slow start. I wasn't very sharp in the beginning. I'm happy I pulled it through, and at this stage it's a good match for me to get through."

Williams had little trouble advancing. She didn't lose a point on serve in the first set and faced just one break point against her serve during the entire match.

"It felt really good," said Williams. "I definitely wouldn't have expected to do so well on serve against her. But I was able to serve really well today."

The other semifinal will feature the other top remaining seeds -- Victoria Azarenka of Belarus and Serbia's Jelena Jankovic.

Azarenka, seeded second this week as she prepares for a run at a third straight Australian Open crown, claimed a 6-4, 6-7 (9-11), 6-1 victory over Switzerland's Stefanie Voegele. The fourth-seeded Jankovic rebounded after a first-set tiebreak loss to earn a 6-7 (8-10), 6-3, 6-1 win over fifth-seeded German Angelique Kerber.