Weather earlier in the week forced a crowded 18-match card for Wednesday, with several players forced to play twice so the tournament could end on schedule Saturday.
However, the final second-round match of the day will have to be completed Thursday, as second-seeded Roberta Vinci and Yulia Putintseva had their match suspended because of darkness. Vinci was about to serve to start the third set when play was stopped.
Zheng opened with a 6-2, 4-6, 6-3 win over Mallory Burdette to earn the right to meet Wozniacki, who had a first-round bye. Zheng had Wozniacki in trouble throughout a 6-2, 6-4 win, forcing 15 break-point chances -- and cashing in five -- on Wozniacki.
She next goes against Romina Oprandi, who was credited with two wins Wednesday. The second came when sixth-seeded Julia Goerges, who had a long first match, retired after Oprandi won the first set 6-3.
Fourth-seeded Sloane Stephens and No. 8 Peng Shuai also won twice Wednesday and will meet in the quarterfinals. Stephens played a 2 1/2-hour, three-setter against Tsvetana Pironkova in her first match but dropped only four games in winning in the second round. Peng's second match was a 4-6, 7-6 (7-4), 7-6 (7-4) battle against Olga Govortsova that took more than 3 hours.
Kaia Kanepi picked up two wins to advance to a quarterfinal versus seventh-seeded Varvara Lepchenko.