Zeel defeated Germany's Jule Niemeier 6-4 6-2 in the second round to set up a contest against fifth seed Serbian Olga Danilovic, who outplayed China's Shuyue Ma 6-3 6-1.
Mihika Yadav is also in the fray. She is up against Japanese 10th seed Mai Hontama.
In the doubles, Zeel and her partner Violet Apisah made an exit after losing 4-6 4-6 to fourth seeds Yang Lee and Rebeka Masarova.
There is no Indian left in the boys singles after first round defeat of Siddhant Banthia against Australia's Alexander Crnokrak.
They next face sixth seeds Zizou Bergs and Yshai Oliel.
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