The fifth-seeded Puig has struggled with consistency since her triumph at the Rio de Janeiro Games, losing in the opening round at the U.S. Open and in her last two tournaments in China.
Four other seeded players were eliminated, including No. 3 Elena Vesnina of Russia, who lost to American qualifier Shelby Rogers 7-5, 4-6, 7-6 (4), and No. 4 Timea Babos of Hungary, who was beaten by another American, Alison Riske, 2-6, 6-4, 6-3.
Peng Shuai of China advanced when seventh-seeded Zhang Shuai withdrew before their match with a lower back injury.