Kvitova was the first to blink at 4-4 as she handed her rival the chance to break. The Czech world number 17 missed out on a break in the next as the unforced errors crept up on her game.
Zhu ran up a 5-4 lead in the second set and appeared on course for a comfortable win before Kvitova produced a flurry of winners to level the contest at 1-1.
World number 113 Zhu went on the attack, taking a 5-3 lead in the decider. She had two chances to seal the match on Kvitova's serve before eventually prevailing.
"I played so relaxed today," Zhu said after the match.
"In the second set I was serving for the match, but she played great to win this, and then I came back in the third set and I played like my first set, and I think I did it!
"I just played my match. I didn't think too much about the win, I just enjoyed the match."
Meanwhile, Maria Sharapova trounced ninth seed Irina-Camelia Begu 6-4 6-2 while China number one Shuai Peng defeated compatriot Hanyu Guo 6-2 7-6(5).
(Reporting by Shrivathsa Sridhar in Bengaluru Editing by Jeremy Gaunt)
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