World number nine Kashyap won his first round match 21-17 21-18 in 43 minutes at the National Indoor Arena. He now runs into seventh seed Kenichi Tago of Japan.
Sourabh Verma, who made it to the main draw after playing in the qualifying round, was the other Indian who made it to the round of 16 in the men's singles event.
Verma beat Dionysius Hayom Rumbaka of Indonesia 10-21 21-14 24-22 in a hard-fought 59-minute duel. He now faces eighth seed Tien Minh Nguyen of Vietnam in the pre-quarters.
In the women's singles, star player Saina Nehwal and P V Sindhu advanced to the round of 16 last night.
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Saina had to sweat it out to beat Sapsiree Taerattanachai of Thailand 21-8 18-21 21-16, while Sindhu registered a relatively easy 21-13 21-18 win over Busanan Ongbumrungpan of Thailand.
In the mixed doubles event, V Diju and Jwala Gutta made it to the pre-quarterfinals with a 21-9 21-17 win over Peter Kaesbauer and Isabel Herttrich of Germany, but the other two Indian pairs -- Akshay Dewalkar and Pradnya Gadre, and Tarun Kona and Ashwini Ponnappa -- fell by the wayside.