The Russian led 2-0 in both sets and 5-4 in the first before Zheng defended three set points and won the remaining 11 points to win the opener 7-5.
Andreeva continued to make mistakes in a second set that was finely poised at 4-4 before Zheng took control.
The crowd was passionate, although disruptive at times between points, and a late double fault from Zheng in the final exchanges briefly threatened to derail a special occasion for Chinese tennis.
But there was to be no late collapse and Zheng sealed the win with an ace.
“I felt like I just forgot how to compete after coming back from injury,” she told reporters.
“Finally, after so many losses, I (found) my fire again,” she said.
The win is her 14th win over a top-10 opponent and her third this season.
Despite the loss, Andreeva is expected to rise to number three in the world when the rankings are updated on Monday.
Zheng is set to leap up 31 spots to number 23 and will compete at Wuhan Open on Tuesday.
“I’m so hungry, honestly, for what’s going to come next,” Zheng said.
“I just want to give everything.”