Samsonova will next face Shuai Zhang, who defeated Petra Martic 7-5, 6-2.
"I'm still working on my technique but most of all my mental game,'' Samsonova said. "I think I've grown up on that part and my team has been amazing. They've really helped me to improve.''
Zheng defeated American player Claire Liu 6-4, 7-5.