While eighth seeded Saina needed only 35 minutes to breeze past Thai Natcha Saengchote 21-15, 21-12, Kashyap beat compatriot R.M.V. Gurusaidutt 21-15, 16-21, 21-11 in 59 minutes in a Round 2 encounter at the Siri Fort Sports Complex.
World No.8 Saina looked in prime form as she moved well on the court, pacing her opponent throughout. After clinching seven straight points to bag the first game, the Hyderabadi dominated the second and finished off the day's work with an irretrievable cross court smash.
Meanwhile, Kashyap equalled his head-to-head against Guru to two-all and will next face the winner of the match between top seed Lee Chong Wei of Malaysia and Sourabh Varma of India.
"After winning the first game I lost my rhythm in the second. I started attacking too much and lost energy. Guru's net and defence play is good. We spar with each other while training, so we know each other's game well. That is why it is always difficult for me to beat him. He has beaten me twice so it was good to beat him," Kashyap said.
Meanwhile, Indonesian Aprilla Yuswandari took only 29 minutes to beat former national champion Trupti Murgunde 21-13, 21-12 in a women's singles clash.
Earlier, India's challenge in doubles competition came to an end when Chinese women fifth seeds Qing Tian and Yunlei Zhao got past India's Jwala Gutta and Ashwini Ponnappa 21-13, 21-19 in 37 minutes.