World number four Badosa, who was recently knocked out in the round of 64 US openstruggled to gain a foothold against 36th-ranked Zheng and joined number two seed Caroline Garcia when leaving the tournament early.
Badosa failed to hit a single ace, losing seven consecutive games before capping off a miserable evening in the Japanese capital by hitting a return straight into the ground at match point.
19-year-old Zheng, who made the last 32 at the US Open, said her win over Badosa was “no surprise” to her.
“I always know I have the level,” Zheng said.
“It’s just the time to make it. I’m so happy to be able to make this match and I want to do it again.”
Zheng, who defeated Japan Misaki Doic 6-2, 6-4 in the first round, now faces Elise Mertens from Belgium or Claire Liu from the United States in the quarterfinals.
Badosa had a bye in the second round.