Lucie Safarova outlasted Venus Williams 6-7 (2), 6-3, 6-4 Tuesday in the first round of the Western & Southern Open.
Suarez Navarro also needed three sets to get past Tsvetana Pironkova 6-3, 1-6, 6-2.
Meanwhile, defending champion Victoria Azarenka withdrew because of a right knee injury, the WTA said. Azarenka withdrew after practicing early Tuesday and was replaced in the draw by Mona Barthel.
Azarenka injured her knee in her first-round win at Wimbledon and played in two tournaments after the grass-court major. She hopes to be ready for the U.S. Open, which starts Aug. 25.
"I'm going to get more treatment and get more work done and should be good for the U.S. Open," Azarenka said in a release. "I feel strongly that it's the best for me at this moment."
In men's play, Marin Cilic advanced to the second round with a 6-3, 6-4 win over Feliciano Lopez, while qualifier James Ward, ranked 148th, upset No. 32 Guillermo Garcia-Lopez, 6-2, 3-6, 6-1.