Zhang, who lost the Wimbledon doubles final with partner Elise Mertens, was broken twice at the start of the second set on Monday before rallying to beat Rebeka Masarova of Spain 7-6 (7-3) 7-6 (9-7).
The Chinese player will face Jasmine Paolini after the Italian eased past Slovakia's Anna-Karolina Schmiedlova 6-3 6-1.
Fourth-seeded Sara Sorribes Tormo is also safely through to the round of 16, with the Spanish player recovering to beat Romanian Ana Bogdan 2-6 6-4 6-2.
The match had to be halted three times, for a medical timeout apiece, and another one due to extreme heat in what was the first match of the day.
Sorribes Tormo will next face Frenchwoman Leolia Jeanjean, who beat Ylena In-Albon 6-2 6-4 of Switzerland.
Sixth-seeded Irina-Camelia Begu of Romania defeated Spain's Marina Bassols Ribera 6-3 4-6 6-3 to set up an encounter against Oceane Dodin of France.
Dodin beat 19-year-old Matilde Paoletti 6-4, 7-5. It was Paoletti's first WTA main draw match and the Italian is assured of moving up around 200 places in the rankings from No.920.
Australia's Jaimee Fourlis, world No.147, opens her campaign in the round of 32 against second-seeded Yulia Putintseva of Kazakhstan on Tuesday.
15°C