Second seed Maria Sharapova powered her way into the third round at Indian Wells with a straight sets victory over Italy's Francesca Schiavone.
The Russian won 6-2 6-1 to set up a meeting with 25th seed Carla Suarez Navarro of Spain.
survived a scare in the second set to beat Olga Govortsova 6-4 3-6 6-3.
The Czech took two hours, 22 minutes to overcome the Belarusian and now faces Ukrainian qualifier Lesia Tsurenko.
The absent Williams sisters
Serena and Venus Williams have not played in Indian Wells since 2001, when Serena was booed in the final after Venus had pulled out minutes before their semi-final. Their father, Richard, later said they had been racially abused.
Tournament director Steve Simon told BBC Radio 5 live sports extra
on Wednesday: "I don't think you ever say it's a lost cause. We have had communications with them over the years, many times, and we actually get along very well with them.
"They unfortunately had, in their minds, a bad experience here and have decided not to come back, but they know that they are welcome here and we get along famously. But they've got their reasons for not wanting to do it, and that's the way it is."
of Poland won through to the third round with a convincing 6-2 6-1 victory against American wildcard Maria Sanchez.
On a cold day in the California desert, world number three Sharapova had too much for former French Open champion Schiavone.
"We broke each other back and forth in the beginning of the first set, and then she had a few opportunities," she said.
"But once I started being a little bit more aggressive I felt like I had an edge on her. She's a tough first round, that's for sure. She likes those centre-court matches. She lives in those opportunities.
"She makes you hit so many balls and she has such a great slice. But, again, that's when she has time to do all that. I try to take that away from her, right from the beginning."
Former world number two
of Russia, ranked 46 after missing six months last year with a knee injury, came back from a disastrous first set to beat Serb 18th seed Jelena Jankovic 0-6 6-2 7-5.
"I was pretty bad in the first set, but I managed to change it," said Kuznetsova, the runner-up in 2007 and 2008. "So I'm pretty happy with it, but I have to change the start."