Zheng edged past Maria Jose Martinez Sanchez 4-6, 7-5, 6-4 in 2 hours, 43 minutes. She had a slight -- 102-99 -- advantage in points taken in the match. Zheng had six breaks, with five coming in the last two sets.
She was able to finish off three of the seven break chances she had in the third set, overcoming two breaks by Martinez Sanchez.
Olga Puchkova was up 6-4, 2-1 when fourth-seeded Francesca Schiavone retired and wild-card entrant Tamarine Tanasugarn had little trouble in posting a 6-3, 6-2 win over fifth-seeded Yaroslava Shvedova.
No. 6-seeded Anabel Medina Garrigues rallied for a 3-6, 6-2, 6-2 victory over Camila Giorgi with three breaks in each the second and third sets. But seventh-seeded Chanelle Scheepers breezed past Alexa Glatch 6-4, 6-1 and No. 8-seeded Laura Robson beat Eleni Daniilidou 6-4, 6-2, losing her serve just once.
Also Tuesday, Virginie Razzano stopped Nudnida Luangnam 6-3, 6-3; Zhou Yi-Miao topped Kurumi Nara 6-5, 6-4; and Mirjana Lucic got by Luksika Kumkhum 4-6, 6-3, 6-4.