Kashyap, seeded 6th, defeated France's Lucas Corvee 21-12 21-17, while Sourabh whipped Canada's B R Sankeerth 21-14 21-11 in another men's singles match.
Kashyap, who had reached the semi-finals at India Open this the year will next meet China's Ren Peng Bo, while 26-year-old Sourabh, who had won titles in Russia and the Netherlands a year ago, faces another Chinese Sun Fei Xiang.
It turned out to be a forgetful day for other Indians in the fray as Ajay Jayaram, HS Prannoy and Lakshya Sen — all bowed out of the competition after losing their respective matches.
While Jayaram went down 19-21 17-21 to 2010 Commonwealth Games silver medallist Rajiv Ouseph of England, third seed Prannoy was no match for Koki Watanabe of Japan, losing 16-21 10-21 of every 34 minutes and Lakshya was dominated by China's Weng Hong Yang 7-21 13-21.
The Indian trio will hope to do well at the US Open BWF World Tour Super 300 event to be held from July 9 to 14.