Home favourite Serena Williams was made to work hard by Yaroslava Shvedova at the WTA Sony Open.
The top seed was taken to a lengthy first-set tie-break but was ultimately comfortable in beating Shvedova 7-6 (9-7) 6-2 to reach the third round.
"She was doing a little bit of everything," Williams said. "She was hitting hard; she was hitting soft; she was doing a little bit of everything.
"I was making a little more errors than what I should have been making, what I should've made, and that kind of threw me for a loop, as well.
"She was up a break (in the first set) and I started just really trying to fight to make the shots. And then when she was serving for the first set I really just tried to be more Serena like."
Maria Sharapova had no trouble getting past Japan's Kurumi Nara, the Russian breaking serve five times to Nara's two in a 6-3 6-4 win.
All the players seeded in the top 20 progressed, though fifth seed Angelique Kerber needed a third-set tie-break before she finally saw off China's Shuai Peng 6-3 1-6 7-6 (7-5).
Petra Kvitova beat Paula Ormaechea 6-3 6-4 while Sara Errani, seeded one place lower at nine, got past Patricia Mayr-Achleitner 6-1 6-4.
Ana Ivanovic ended the hopes of American Lauren Davis, winning 6-1 6-1, while Sabine Lisicki came from a set down to beat wild card Nadia Petrova 3-6 6-4 6-4.
There were three seeds eliminated, with Anastasia Pavlyuchenkova the highest at 21 as qualifier Coco Vandeweghe delighted the home fans with a 7-6 (9-7) 7-5 win.
Tsvetana Pironkova beat 25th seed Sorana Cirstea 6-3 6-3 while Carolina Garcia saw off Klara Zakopalova in two tie-breaks.
And 17-year-old Croatian qualifier Donna Vekic marched on with a 7-6 (7-5) 7-5 win over Svetlana Kuznetsova, the 28th seed.
Sam Stosur, Ekaterina Makarova, Kirsten Flipkens, Lucie Safarova and Flavia Pennetta all went safely through, with Flipkens the only one of the quintet to drop a set.