Zheng dispatched Sakkari in one hour, 49 minutes to punch her ticket to the next round.
She will face Ukraine's Anhelina Kalinina, who posted a 7-5, 6-1 victory over Russian qualifier Vera Zvonareva.
Italy's Jasmine Paolini saved four match points in a 3-6, 6-4, 7-5 win over sixth-seeded Caroline Garcia of France, while Ukraine's Lesia Tsurenko notched a 7-6(4), 7-6(2) win over 10th-seeded Donna Vekic of Croatia.
Hana Bank Korea Open
Belgium's Yanina Wickmayer seized a 6-3, 7-6(5) victory over third-seeded Ekaterina Alexandrova of Russia to move on to the quarter-finals in Seoul.
Wickmayer will meet Russian Polina Kudermetova, who breezed to a 6-3, 6-1 win over Kathinka von Deichmann (20) of Liechtenstein.
Also on Wednesday, Claire Liu led seventh-seeded Arantxa Rus of the Netherlands 1-6, 6-3, 3-0 when the latter retired due to injury. China's Yuan Yue also advanced after Slovenia's Kaja Juvan retired while trailing 6-4, 4-1.
Hong Kong Open
Second-seeded Beatriz Haddad Maia of Brazil posted a 7-6(3), 3-6, 7-6(3) win over Belarus' Aliaksandra Sasnovich in their first-round match.
Fifth-seeded Anna Blinkova of Russia coasted to a 6-1, 6-3 win over Australian Priscilla Hon to advance to the third round.
Third-seeded Elise Mertens of Belgium had little difficulty in her 6-1, 6-4 victory over Australian qualifier Daria Saville.