World number two Saina defeated Belaetrix 21-16 21-11 in a 34-minute match at the National Indoor Arena here. The 22-year-old will next take on sixth seed Chinese Shixian Wang tomorrow.
Rising Indian shuttler P V Sindhu, however, crashed out after suffering a straight-game defeat to fourth seed Juliane Schenk of German in the prequarterfinals of the USD 400,000 Super series premier tournament.
World number 16 Sindhu suffered a 17-21 14-21 loss to the German in a 39-minute women's singles match here. Juliane rode on her smashes and better net play to outdo the Indian.
World number nine Kashyap won his first round match 21-17 21-18 in 43 minutes. He now runs into seventh seed Kenichi Tago of Japan later tonight.
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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 later.
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.
Dewalkar and Gadre lost to Malaysian combination of Jian Guo Ong and Yin Loo Lim 8-21 13-21, while Kona and Ponnappa were beaten 18-21 10-21 by Fran Kurniawan and Shendy Puspa Irawati of Indonesia.