Kashyap crossed the second round after his opponent Hungary's Gergely Krausz retired midway in the second game with the scoreline reading 21-18 17-6 in favour of the Indian.
The Commonwealth Games champion then defeated Sri Lanka's Niluka Karunaratne, seeded 16th, 21-19 21-10 in the prequarterfinals match on the same day.
Kashyap will next face compatriot and fifth seed Sameer Verma, who notched up victories over Croatia's Zvonimir Durkinjak and Brazil's Ygor Coelho.
Sameer, who is making a comeback after recovering from a shoulder injury, had to fight hard to get the better off Zvonimir 21-19 25-27 21-15 in the first match. He then saw off ninth seed Ygor 18-21 21-14 21-18.
Second seed H S Prannoy, meanwhile, brushed aside Ireland's Joshua Magee 21-13 21-17 before staving off a challenge from Netherlands' Mark Caljouw, seeded 12th, 21-8 14-21 21-16 in 48 minutes.
Prannoy will face eighth seed Kanta Tsuneyama of Japan next.
Among other Indians in fray, third seeds Manu Attri and B Sumeeth Reddy defeated Indonesian combo of Hendra Tandjaya and Androw Yunanto 21-16 21-9 to set up a clash with seventh seeded Japanese Hiroki Okamura and Masayuki Onodera.
It was however curtains for Harsheel Dani, Sri Krishna Priya Kudaravalli, Rituparna Das in singles event.
Vietnam's Tien Minh Nguyen ended Harsheel's stay with a 27-25 21-9 win, while Sri Krishna lost 11-21 10-21 to fifth seed Jang Mi Lee of Korea and Rituparna suffered a 15-21 20-22 loss to seventh seed Natalia Koch Rohde of Denmark.
Men's doubles pair of Francis Alwin and Tarun Kona fought hard before losing 19-21 21-9 14-21 to seventh seed Hiroki Okamura and Masayuki Onodera of Japan.
Women's doubles pair of Meghana Jakkampudi and Poorvisha S Ram also bowed out with a 18-21 9-21 loss to seventh seeds Mayu Matsumoto and Wakana Nagahara of Japan.
Mixed doubles pair of Manu and Maneesha also suffered a 16-21 12-21 loss to fourth seeded Malaysian combo of Goh Soon Huat and Shevon Jemie Lai.
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