World number 16 Sindhu, who is the lone Indian woman in the fray in the absence of star compatriot Saina Nehwal, came back from a game down to win 15-21 21-14 22-20 in a tense contest.
It took the unseeded Indian an hour and two minutes to overcome the current world No. 6 Chinese in what was their first-ever encounter.
Sindhu will take on seventh seed Eriko Hirose of Japan in the last-eight stage of the competition.
Earlier, in the second round of the men's singles event, Kashyap got the better of Han Chou Chu of Taipei 21-17 21-19 in 31 minutes.
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He will play his third round match later today against 15th seeded Huan Gao of China.
Sai Praneeth B, however, failed to cross the second round hurdle, going down 15-21 16-21 to sixth seeded Zhengming Wang in 36 minutes.
Yesterday, all other Indian combinations in men's, women's and mixed doubles categories had already lost their respective first round ties.