Zhang secured her first WTA title last week in Guangzhou, and after defeating fellow Chinese Zheng, 61 61, has now won 14 straight sets.
"I think I played well today," Zhang said. "Going back to Guangzhou, I have played better and better each match."
Zhang has surrendered just five games through two matches this week.
"Zhang played really well today," Zheng said. "She hit the ball hard and moved well. It was very difficult for me to win points. I did have chances today, but didn't take them.
"She won the title in Guangzhou, which gave her a lot of confidence. If she can keep playing like this, she will make it into the Top 30 soon."
Zhang also competed in Ningbo when it was an ITF Women's Circuit event before it was upgraded to a WTA 125K Series event this year.
"This is the third time I've been to Ningbo," Zhang said. "I really enjoy playing here and hope I can keep playing better."
Wednesday's other quarterfinals will see Zhang take on Anabel Medina Garrigues, Larsson square off with Johanna Konta and No.1 seed Bojana Jovanovski play Anna Schmiedlova. Jovanovski didn't have to take the court for her second round match, as scheduled opponent Shahar Peer withdrew with a left foot injury.