Zheng dispatched Sakkari in one hour, 49 minutes to punch her ticket to the next round.
She will face Ukraine's Anhelina Kalinina (26), who posted a 7-5, 6-1 victory over Russian qualifier Vera Zvonareva (39).
Italy's Jasmine Paolini (27) saved four match points in a 3-6, 6-4, 7-5 win over sixth-seeded Caroline Garcia (29) of France, while Ukraine's Lesia Tsurenko (34) notched a 7-6, 7-6 win over 10th-seeded Donna Vekic (27) of Croatia.
Hana Bank Korea Open
Belgium's Yanina Wickmayer (33) seized a 6-3, 7-6 victory over third-seeded Ekaterina Alexandrova (28) of Russia to move on to the quarterfinals in Seoul.
Wickmayer will meet Russian Polina Kudermetova (29), who breezed to a 6-3, 6-1 win over Kathinka von Deichmann (20) of Liechenstein.
Also on Wednesday, Claire Liu (23) led seventh-seeded Arantxa Rus (32) of the Netherland 1-6, 6-3, 3-0 when the latter retired due to injury. China's Yuan Yue (25) also advanced after Slovenia's Kaja Juvan (22) retired while trailing 6-4, 4-1.
Hong Kong Open
Second-seeded Beatriz Haddad Maia (27) of Brazil posted a 7-6, 3-6, 7-6 win over Belarus' Aliaksandra Sasnovich (29) in their first-round match.
Fifth-seeded Anna Blinkova (25) of Russia coasted to a 6-1, 6-3 win over Australian Priscilla Hon (25) to advance to the third round.
Third-seeded Elise Mertens (27) of Belgium had little difficulty in her 6-1, 6-4 victory over Australian qualifier Daria Saville (29).
