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The world No. 9, Prannoy, eked out a 21-19, 22-20 win over Wang in the 49-minute opening round clash to take his overall tally to 5-3 over the Taiwanese.
Lakshya, seeded seventh, came from a game down to win 19-21, 21-8, 21-17 against Malaysia's NG Tze Yong.
Former world No. 1 Kidambi Srikanth continued to flatter to deceive as he blew an 18-15 lead and two game points to lose to Indonesia's Shesar Hiren Rhustavito 10-21, 22-24.
Defending champion Lakshya Sen and former champion Saina Nehwal suffered contrasting defeats in their respective second round matches.
Two-time Commonwealth Games champion Saina went down 12-21, 21-17, 12-21 to Han Yue of China.
He became only the fourth Indian to win a silver medal in the competition.
The two Indian men's doubles pair of Dhruv Kapila and M R Arjun and Satwiksairaj Rankireddy and Chirag Shetty also moved into the quarterfinals.
The women's doubles pair of Treesa Jolly and Gayatri Gopichand also made a winning start.
Sindhu will next face unseeded Saena Kawakami, the Japanese world No. 38, who caused an upset by eliminating sixth-seeded Pornpawee Chochuwong of Thailand 21-17 21-19.
For Saina Nehwal it is consecutive first-round exit in the event.