She will face France's former Wimbledon finalist Marion Bartoli, who beat Yanina Wickmayer 6-4, 7-5.
Meanwhile, Marion Bartoli needed only eight games to beat Jelena Jankovic, who retired feeling unwell.
Cavaday's reward for beating Bardina is a meeting with fifth seed Marion Bartoli of France.
Ivanovic, the 2008 Indian Wells winner, beat French seventh seed Marion Bartoli 6-3 6-4 in their quarterfinal.
She next plays unseeded Francesca Schiavone, the 2010 champion, who beat No. 13 Marion Bartoli of France 6-2, 6-1.
At the WTA event in Paris, France's Marion Bartoli will face Germany's Angelique Kerber in the final on Sunday.
The Williams sisters Venus and Serena are not playing, nor is Bank of the West Classic winner Marion Bartoli.
Seventh seed Marion Bartoli awaits Ivanovic in the last eight, following the Frenchwoman's win over Czech No. 23 Lucie Safarova.
The Italian, also the 2011 runner-up but now dropped to 50th in the rankings, crushed French 13th seed Marion Bartoli 6-2 6-1.
Kvitova's win sets up a match against another French opponent, Marion Bartoli.
The Australian lost in straight sets, 6-4 6-2, to American Laura Granville, with ninth seed Marion Bartoli losing 6-3 6-0 to Thai Tamarine Tanasugarn.
However, 15th seed Marion Bartoli was the second seed to fall on Wednesday when she was beaten 3-6 6-3 6-0 by Russia's Vesna Manasieva .
Meanwhile, Marion Bartoli of France beat Anabel Medina Garrigues of Spain 6-2 6-1 and seventh-seeded Marlene Weingartner of Germany eased past Aranxta Parra of Spain 6-2 7-5.
The 22-year-old won 7-5 7-6 (7-4) against the 2012 French Open runner-up as she followed up earlier victories over third seed Marion Bartoli and No. 5 Roberta Vinci.
Russian second seed Anna Chakvetadze beat Israeli Shahar Peer 6-3 6-4 and plays the winner of Thursday's second-round match between French sixth seed Marion Bartoli and Britain's Anne Keothavong.
Henin has a 12-11 advantage in matches between the two, and the winner of Thursday night's match will take on either American third seed Venus Williams or France's No. 13 Marion Bartoli.
Ninth seed Marion Bartoli beat fellow Frenchwoman Virginie Razzano 7-5 6-0 and will next face Australia's former world No. 4 Jelena Dokic, who won 6-2 6-1 against 196th-ranked Russian Anna Chakvetadze -- a quarterfinalist in 2007 on her way to a career-high No. 5.
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