She has lost Key Biscayne finals to Kim Clijsters, Svetlana Kuznetsova, Victoria Azarenka and Agnieszka Radwanska.
Poland's Agnieszka Radwanska eased into the quarterfinals when she beat Hungary's Greta Arn of Hungary 6-3, 6-4.
Eighth seed Agnieszka Radwanska , a quarterfinalist in 2011, came from behind to eliminate American Bethanie Mattek-Sands.
In the women's tournament, Venus Williams advanced to the semi-finals with a 6-3 6-1 victory over Agnieszka Radwanska.
Top seed Azarenka beat Poland's Agnieszka Radwanska 6-3, 6-3 in the other semifinal.
Czech eighth seed Petra Kvitova, the 2011 Madrid champion, went through to round two along with Poland's world No. 4 Agnieszka Radwanska.
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The No. 3 seed, Agnieszka Radwanska from Poland, wasted little time in wrapping up a 6-3 6-3 win over Slovakia's Magdalena Rybarikova.
The American will play Victoria Azarenka in the final after the Belarusian overcame Poland's Agnieszka Radwanska in straight sets in the second semi-final.
Defending champion and No. 4 seed Agnieszka Radwanska, from Poland, breezed into round three with a 6-3 6-2 victory over Taiwan's Hsieh Su-Wei.
Polish sixth seed Agnieszka Radwanska defeated former world No. 1 Ana Ivanovic 7-5 7-5 to set up a clash with Kazakhstan's Yaroslava Shvedova.
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She is followed by world number two Victoria Azarenka of Belarus and Poland's Agnieszka Radwanska, with reigning Wimbledon champion Petra Kvitova seeded fourth.
The world No. 26 will next play fellow left-hander Lucie Safarova after the Czech upset Polish eighth seed Agnieszka Radwanska 1-6 6-3 7-6 (7-2).
The 2013 calendar sees the circuit return to Poland -- home of world No. 4 Agnieszka Radwanska -- for the first time since 2010.
Fourth-ranked Agnieszka Radwanska sent out a warning to the top three by thrashing Dominika Cibulkova 6-0 6-0 in Friday's final of the Sydney International.
It is the first time Kirlenko has made the final four at Indian Wells following wins over Agnieszka Radwanska and former Wimbledon champion Petra Kvitova.
Kirilenko will meet third seed Agnieszka Radwanska of Poland in the quarter-finals, while top seed Samantha Stosur of Australia will play Yanina Wickmayer of Belgium.
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The 2010 runner-up, who had beaten the Serbian 15th seed in seven of their previous eight meetings, will next face Polish fifth seed Agnieszka Radwanska.
Fourth seed Agnieszka Radwanska eased past Irina-Camelia Begu, while there were also wins for German fifth seed Angelique Kerber and China's sixth seed Li Na .
Maria Sharapova, seeded second, will take on fellow Russian Olga Puchkova in round one and could face Polish fourth seed Agnieszka Radwanska in the final four.
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Meanwhile at the WTA clay-court event in Stuttgart, world number one Victoria Azarenka has reached the final after cruising past Agnieszka Radwanska 6-1 6-3 in Saturday's semifinals.
The teenager had only got to bed at 1am after losing her doubles quarter-final alongside Sally Peers against Maria Kirilenko and Agnieszka Radwanska late on Wednesday evening.
Chakvetadze will take on Polish eighth seed Agnieszka Radwanska in the last 16, with the winner to then play either German 17th seed Sabine Lisicki or unseeded Romanian Sorana Cirstea.
Seeds Agnieszka Radwanska, Flavia Pennetta, Alisa Kleybanova, Agnes Szavay, Sybille Bammer and Aleksandra Wozniak also advanced, but Alize Cornet, Dominika Cibulkova, Zheng Jie, Ai Sugiyama and Sara Errani failed to progress.
In the women's draw, Li Na beat defending champion Agnieszka Radwanska of Poland 6-4 6-2 to secure reach the semifinals and seal her place in the season-ending WTA Championships in Istanbul.
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In the evening's other match Agnieszka Radwanska, the No. 4 seed from Poland, booked a semifinal with Serena Williams after recording an epic 6-7 7-5 6-4 victory over Italian Sara Errani.
Williams will now face world number six Victoria Azarenka of the Belarus, who came back from 2-4 down in the second set to complete a 6-3 6-4 win over Agnieszka Radwanska of Poland.
But Williams, a seven-time grand slam title winner, faces a tough second round match against fancied third seed Agnieszka Radwanska, if the Pole can get past Bojana Jovanovski of Serbia in her opener.
Next up for Belarus' Azarenka is Polish fifth seed Agnieszka Radwanska , who benefited from the retirement of American wildcard Jamie Hampton due to cramps in the third and deciding set of their match.
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