World number one Iga Swiatek is through to the third round at Indian Wells, while Angelique Kerber’s successful comeback continues.
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 German former world number one gave birth to her 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 607th – this is just her fourth event since she returned to the WTA Tour at the end of December.
Denmark’s Caroline Wozniacki, who also recently returned to the tour after becoming a mother, also progressed with a 7-6 (7-5) 6-3 win over Donna Vekic.
American Katie Volynets, ranked 131st in the world, pulled off a major upset after she beat Tunisian sixth seed Ons Jabeur 6-4 6-4.
Another contender who was knocked out in the second round was Russian 15th seed Ekaterina Alexandrova, beaten 7-5 6-1 by Kazakhstan’s Yulia Putintseva.
Wimbledon champion Marketa Vondrousova of the Czech Republic, seeded seventh, went through 6-0 6-2 against American Bernarda Pera.
Italian Jasmine Paolini eased to a 6-3-6-3 win over Germany’s Tatjana Maria while Russian Veronika Kudermetova clinched a 6-1 7-5 win over Japan’s Nao Hibino.