China's Zheng, seeded seventh, next faces Erika Andreeva of Russia, who beat China's Yuan Yue 6-3, 7-6 (9/7).
"Obviously she's hitting the ball really good today," Zheng said of Anisimova, who is on the upswing since returning from a mental health break in January -- when she was ranked 373rd in the world. A run to the final at Toronto this month saw her return to the top 50 and gain a wild card invitation into the main draw.
"Every ball (from Anisimova) went inside in the beginning and I couldn't do anything," Zheng said. "More as the match goes I started to find my rhythm on hard court. Little by little I started to get into the rhythm."
Zheng, who finished runner-up to Aryna Sabalenka at the Australian Open in January, has said she didn't want the same let-down that followed that performance happen in the wake of her groundbreaking Paris Games triumph.
Asked on court about her run to gold -- which made her China's first Olympic tennis singles champion -- she was gracious but already looking forward.
"I'm happy what I did in the past, but right now I just want to focus on what I do here," said Zheng, who could face Sabalenka again in the quarter-finals.
