Zhang Shuai and Sabine Lisicki came through their Hawaii Open first-round matches as two seeds fell on Tuesday.
Zhang, the top seed, had few problems getting past Japan's Akiko Omae 6-3 6-2 on the hard courts in Honolulu.
German Lisicki, the 2013 Wimbledon runner-up, beat Julia Boserup 6-4 6-4 at the WTA 125K event, being played for the first time.
But Nicole Gibbs and Maria Sakkari made early departures.
Second seed Gibbs went down to fellow American Jacqueline Cako 6-3 7-5 and Sakkari was beaten by Sachia Vickery 7-5 6-2.
Samantha Crawford, the eighth seed, was too good for Erika Sema 6-3 6-4.
Meanwhile, Marina Erakovic overcame Danielle Lao 6-3 6-4, Tatjana Maria retired while 6-2 3-0 down to Danielle Collins and Eri Hozumi beat Olga Govortsova 6-2 6-3.
Asia Muhammad cruised past Hiroko Kuwata 6-3 6-1, Veronica Cepede Royg beat Grace Min 6-3 6-4 and Jamie Loeb had a 6-2 6-4 win over Ingrid Neel.