Two-time World Championships bronze medallist Sindhu took just 31 minutes to get the better of Ksenia Polikarpova of Russia 21-17 21-19 at the Odense Sports Park.
Srikanth defeated Chinese Taipei's Jen Hao Hsu 21-12 21-15 in 45 minutes while Kashyap fought hard before prevailing over Dionysius Hayom Rumbaka of Indonesia 21-17 17-21 22-20 in a contest that lasted 69 minutes.
World No. 10 Sindhu opened up a 4-0 lead in the first game and continued to widen the gap, eventually winning it 20-17.
In men's singles second round matches, Srikanth had a rather comfortable outing today, but Glasgow Commonwealth Games gold medallist Kashyap faced a stiff challenge from his Indonesian rival.
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After a neck and neck battle till 13-13 in the opening game, Kashyap bagged four consecutive points to make it 17-13 and then there was no looking back for the Indian.
Although Kashyap managed to reel off six points on a trot to catch his opponent, the Indonesian showed a lot of determination to keep the Indian at bay and take the match to the decider.
Third game was a closely-fought affair with both players refusing to spare an inch. The game swung from one end to other before the Indian held his nerves to earn two points from 20-20 to advance to the next stage.