World number one Caroline Wozniacki will hope to win her first grand slam title at the Australian Open. starting next week.

Story highlights

Caroline Wozniacki and Petra Kvitova both win as they battle for world No. 1 spot

Wozniacki defeats Dominika Cibulkova, while No. 2 Kvitova beats Alexandra Dulgheru

Kvitova will usurp Wozniacki with victory at the Australian Open warm-up event

Former world No. 1 and two-time grand slam winner Lleyton Hewitt beaten by Viktor Troicki

CNN  — 

World No. 1 Caroline Wozniacki and No. 2 Petra Kvitova both earned hard-fought wins at the Sydney International on Tuesday as the battle for the top spot in women’s tennis intensifies ahead of the Australian Open.

Top seed Wozniacki recovered from 0-4 down in the deciding set to beat Slovakia’s Dominika Cibulkova 7-5 2-6 6-4, while 2011 Wimbledon champion Kvitova scrapped to a 7-5 3-6 6-4 victory over Romania’s Alexandra Dulgheru.

Denmark’s Wozniacki has finished the past two seasons top of the world rankings, despite not winning a grand slam title, having first risen to the summit in October 2010.

But rising Czech star Kvitova can usurp her fellow 21-year-old by winning the Sydney event before the season’s first grand slam starts in Melbourne next week. The draw means the top-seeded duo cannot meet until Friday’s final.

“I felt like everything I tried to do wasn’t working and I was making a lot of unforced errors,” Wozniacki told the WTA Tour’s website. “So I said, ‘Okay, let’s just keep a margin to the lines and give her that extra ball.’ It paid off in the end.

“That I could fight back from that score and win is definitely satisfying, but I’ll need to step my game up a little bit in the next round.”

Kvitova dismissed talk of claiming the top ranking for the first time in her career, instead insisting she is taking the tournament one match at a time.

“I’m not really focused on the first spot,” she said. “This tournament is very tough and everybody is playing here. It’s like the final rounds of a grand slam, so it’s not easy to win these matches. So it’s only words.”

Wozniacki will play Poland’s Agnieszka Radwanska in the quarterfinals, after the 22-year-old defeated Germany’s Andrea Petkovic 7-5 6-4.

Kvitova faces Slovakia’s Daniela Hantuchova, who beat Italy’s 2010 French Open champion Francesca Schiavone 7-5 6-1.

Third seed Victoria Azarenka defeated Serbia’s former world number one Jelena Jankovic 6-4 6-2 to set up a clash with French eighth seed Marion Bartoli – who eliminated Australia’s Jelena Dokic 6-0 6-3.

China’s defending champion Li Na came from a set down to win 2-6 6-4 6-1 against South Africa’s Chanelle Scheepers.

The 2011 French Open winner, seeded fourth, will next play the Czech Republic’s Lucie Safarova, who advanced when Russia’s Svetlana Kuznetsova retired with heat exhaustion.

In the men’s draw, fifth seed Viktor Troicki beat home favorite and two-time grand slam winner Lleyton Hewitt 4-6 6-3 6-2 in the first round.

The Serbian earned a clash with Russia’s Alex Bogomolov Jr., who won 6-4 1-6 6-4 against the Netherlands’ Robin Haase.

Czech eighth seed Radek Stepanek also registered an opening victory, defeating Belgium’s Xavier Malisse 6-7 (4-7) 6-4 6-4.

In Tasmania, Belgium’s Yanina Wickmayer justified her tag as top seed at the Hobart International by destroying Australian wildcard Casey Dellacqua 6-1 6-1 in the second round on Tuesday.

Former world No. 5 Anna Chakvetadze also went through to the quarterfinals with a 6-3 6-2 win over Bulgaria’s Tsvetana Pironkova, while 2011 finalist Bethanie Mattek-Sand of the U.S. was beaten 2-6 6-3 7-5 by Romania’s Sorana Cirstea.

Israeli sixth seed Shahar Peer, the 2010 runner-up, won her first-round match 6-3 6-1 against the Czech Republic’s Lucie Hradecka.