Wozniacki can retain her top ranking if she reaches the last four in Melbourne.
In March, Jankovic beat Caroline Wozniacki to win the BNP Paribas Open at Indian Wells.
"I just kept fighting for every point, " Wozniacki told the official WTA Tour Web site.
The 23-year-old was joined on the list by his tennis star girlfriend Caroline Wozniacki.
Wozniacki took the defeat in her stride as she moves on to the clay court season.
Venus Williams, Caroline Wozniacki and Victoria Azarenka are also participating in the event in Hong Kong.
Denmark's Caroline Wozniacki, Azarenka and Russia's Nadia Petrova, ranked 8-10, also received first-round byes.
He is young and charismatic with a famous girlfriend in former No. 1 tennis player Caroline Wozniacki.
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Wozniacki said she would have to perform well to beat Radwanska, who she last faced in 2008.
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World number one Wozniacki of Denmark then thrashed Russia's Elena Dementieva 6-1 6-1 in the Maroon Group.
Cibulkova, the 29th seed, beat Wozniacki in her first competitive match of 2011 in Sydney last week.
Clijsters' breakthrough in the second set came after breaking Wozniacki to lead 4-2 and take the next game.
Henin came from behind to oust second seed Caroline Wozniacki, beating the young Dane 6-7 (5-7) 6-3 6-4.
There were a host of other explanations, sensible or wild, including his romance with tennis star Caroline Wozniacki.
"She just went for every shot and hit it deep, and I came under pressure straightaway, " Wozniacki added.
In the documentary, McIlroy's tennis star girlfriend, Caroline Wozniacki, also gives a unique insight into the couple's relationship.
Earlier Zheng's compatriot Li Na followed her into the quarterfinals after stunning fourth seed Caroline Wozniacki in straight sets.
The group who met the Queen also included Venus Williams, Caroline Wozniacki, Jelena Jankovic, Novak Djokovic and Andy Roddick.
Wozniacki, who has 20 WTA titles to her name, is now hoping to bounce back in Miami next week.
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Caroline Wozniacki also advanced with a 6-1 6-0 win over American Vania King.
Denmark's Wozniacki eventually outmuscled Pennetta in three hours despite the Italian hitting more than twice the number of winners.
Sharapova, 25, started at breathtaking speed, pummeling her opponent with a degree of power which gave Wozniacki little chance.
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But it is Wozniacki's achievements on the court which still create the biggest news, not all of it positive.
Cirstea beat Caroline Wozniacki and Jelena Jankovic on her way to the last eight at Roland Garros last year.
The No. 1 ranked player the past three years has included Ana Ivanovic, Jelana Jankovic, Dinara Safina and Carolyn Wozniacki.
Caroline Wozniacki, once the No. 1 tennis player in the world, has been linked to McIlroy for nearly two years.
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Zheng's compatriot Li Na followed her into the quarterfinals on Monday after stunning fourth-seeded Dane Caroline Wozniacki in straight sets.
Wozniacki, 19, moves on to the last eight where she will play Nadia Petrova, who beat Aleksandra Wozniak 6-2 6-4.
Unfortunately for fourth-ranked Wozniacki, her Russian opponent was not so generous to her and closed out a 6-3 6-4 victory.
She beat Caroline Wozniacki in the Indian Wells final a week ago and has a record of 16-2 this year.
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