Former world number one Victoria Azarenka took nearly three hours to book her place in the next round of the Mudabala Silicon Valley Classic.
The Belarussian beat Kateryna Bondarenko 6-3 6-7 (9/7) 7-5 in the first round in San Jose, her first hard court tournament since March's Miami Open.
Azarenka will play Garbine Muguruza in the next round.
Elsewhere, there were straight-sets wins for Danielle Rose Collins, Alja Tomljanovic, Sofia Kenin and Maria Sakkari.
At the Citi Open in Washington DC, Germany's Andrea Petkovic defeated American Jamie Loeb 6-1 6-1 and Russian Svetlana Kuznetsova swept aside another American, Kristie Ahn, 6-2 6-1.
There were also victories for Katie Boulter, Allie Kiick and Fanny Stollar.