The Williams sisters are level with Switzerland's Martina Hingis and Justine Henin of Belgium.
Safina's defeat follows the first-round exits of big stars Justine Henin, Maria Sharapova and Svetlana Kuznetsova.
Belgians Kim Clijsters and Justine Henin, seeded one and two for the tournament, both received first-round byes.
Justine Henin also picked up a knock in Belgium's 3-2 victory over Estonia.
In the day's final tie Belgium , without Justine Henin-Hardenne and Kim Clijsters, took the lead against Spain .
Since Justine Henin won her last title in 2007, there have been five different French Open champions in five years.
Davenport's next opponent will be Justine Henin , the Belgian fourth seed who defeated Marie-Gaianeh Mikaelian of Switzerland, 7-5, 6-2.
"Somebody like Justine Henin is playing good tennis but in terms of marketability she's not quite up there, " he says.
Sharapova's victory means she will meet her compatriot Anna Chakvetadze in the semi-finals, while Ivanovic plays defending champion Justine Henin.
Williams will now meet Kim Clijsters in the final, after the Belgian saw off compatriot Justine Henin in three tough sets.
Clijsters will now play fellow countrywoman Justine Henin-Hardenne , the third seed, who eased past the unseeded Russian Svetlana Kuznetsova 6-1 6-3.
Clijsters, who defeated fellow comeback queen Justine Henin in an epic semifinal on Friday, broke Williams to love to seal the title.
Neither did Martina Hingis, Justine Henin, Venus Williams or Lindsay Davenport.
But after failing to advance past the fourth round at any major in 2012, Li hired Carlos Rodriguez, Justine Henin's former coach.
In the remaining quarter-finals, Svetlana Kuznetsova beat Patty Schnyder 6-3 6-4 and will face top seed Justine Henin, who thrashed Elena Daniilidou 6-0 6-2.
The event, which is viewed as a warm-up for the Australian Open, will also feature players such as Novak Djokovic, Serena Williams and Justine Henin.
Clijsters was also beaten in four Grand Slam finals including the 2004 Australian Open to compatriot and rival Justine Henin, who has also since retired.
U.S. Open champion Clijsters avoided suffering the same demise as fellow Belgian and former world No. 1 Justine Henin, who lost to Argentina's Gisela Dulko on Friday.
Meanwhile, Justine Henin will take on fellow Belgian Kim Clijsters in a battle of the former number ones in the semifinals of the women's event in Miami.
ATHENS, Greece -- World No 1 Justine Henin-Hardenne of Belgium overcame France's Mary Pierce 6-4 6-4 to set up an Olympic semifinal with French Open champion Anastasia Myskina.
Justine Henin, Kim Clijsters and Serena and Venus Williams each won at least five titles and 86% of their matches in the year after reaching the top.
In the women's tournament, Kim Clijsters and Justine Henin made it a good day all-round for Belgium as the former world No. 1s progressed into the third round.
CNN: Djokovic dumped out in Miami; Clijsters and Henin progress
And although she could lose her number one ranking to compatriot Justine Henin-Hardenne this week, Clijsters believes the younger Williams sister is the best player in the world.
Earlier this year, she suffered the heaviest Grand Slam defeat of her career when she was thrashed 6-0 6-1 by Belgian Justine Henin-Hardenne in the Australian Open second round.
ATHENS, Greece -- Defending Olympic champion Venus Williams and world number one Justine Henin-Hardenne were drawn to face each other in a potential quarterfinal at the Olympic tournament in Athens.
Her victory was slightly devalued by the fact that her opponents in both the semi-final and final - Kim Clijsters and Justine Henin - had to retire through injury or illness.
And so it's time to stop asking whether women's tennis will ever have another champ in the mold of Martina Navratilova, Steffi Graf, Monica Seles, Martina Hingis, the Williams sisters, Justine Henin.
The Belgian was joined in the next round by compatriot and wildcard Justine Henin, although the former world number one was made to battle a bit harder before edging past Dominika Cibulkova 6-4 6-4.
Li, a badminton convert and journalism graduate, attributes some of her newfound consistency and calm to coach Carlos Rodriguez, who guided Justine Henin to seven major titles, including the Australian Open nine years ago.
Clijsters won the U.S. Open last September in fairytale comeback after more than two years out of action, could meet fellow Belgian Justine Henin in the final as they are on opposite sides of the draw.
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