World number one Iga Swiatek is through to the third round at Indian Wells, while Germany’s Angelique Kerber continued her comeback with success.
Poland’s Swiatek beat Danielle Collins 6-3 6-0, having broken the American’s serve to make it 5-3 before breezing through the second set.
Kerber, 36, recovered to beat Latvia’s 10th seed Jelena Ostapenko 5-7 6-3 6-3.
However, reigning women’s champion Elena Rybakina withdrew before her opening match because of illness.
Rybakina was due to face Argentina’s Nadia Podoroska.
Victory was only Kerber’s third since the former world number one gave birth to a first child just over a year ago.
Three-time Grand Slam winner Kerber reached the top of the world rankings in 2016, but is currently ranked 607 as this is just her fourth event since returning to the WTA Tour at the end of December.
Another favourite to be knocked out in the second round was Russia’s 15th-seed Ekaterina Alexandrova, beaten 7-5 6-1 by Kazakhstan’s Yulia Putintseva.
But the Czech Republic’s Marketa Vondrousova, the seventh seed, went through 6-0 6-2 against the USA’s Bernarda Pera.