Zheng, No. 157 in the rankings, got nearly two-thirds of the points on serve in improving to 2-0 lifetime against Garcia with a 6-4, 6-4 win. Zheng also won in two sets in a match in Taiwan last year.
She was able to finish off half of her six break chances in advancing.
No. 7-seeded Ajla Tomljanovic won by the same 6-4, 6-4 score, beating Olga Puchkova. Tomljanovic managed just two break points but cashed in both for the win.
Eighth-seeded Anna Schmiedlova topped Risa Ozaki 7-5, 6-4 despite eight double faults and dropping serve six times. Schmiedlova, however, won 61 percent of the points when Ozaki served and had eight breaks in 11 receiving games.
Also, Irina-Camelia Begu stopped Daria Gavrilova 2-6, 6-4, 6-2; Alla Kudryavtseva raced past Tereza Mrdeza 6-4, 6-0; and Anna-Lena Friedsam edged Katarzyna Piter 6-7 (4-7), 6-1, 7-6 (7-3).
No. 55-ranked Kimiko Date-Krumm is the No. 1 seed for the new tournament.