The 23-year-old from Hyderabad registered an easy 21-7 21-13 win over Sashina Vignes Waran of France in the pre-quarterfinals that lasted 34 minutes in the women's singles competition.
Kashyap, on the other hand, had to toil hard before prevailing over Malaysia's Beryno Jiann Tze Wong 21-23 21-9 21-14 in a 57-minute men's singles match at St. Jakobshalle. He will next take on Chinese Taipei's Tien Chen Chou in the quarterfinals.
In the second game, the sixth seeded Indian was chased by the World number 42 French from 3-8 to 11-12, but Saina reeled off six points at 15-13 to seal her place in the quarterfinals.
The World number eight Indian has a poor record against Yihan, losing six times and her only victory was at the London Olympics when the Chinese had retired midway because of a knee injury.
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In the second game, the 27-year-old showed his class as he didn't allow the Malaysian any chance to come near and led right from the start to make a roaring comeback in the contest.
In the decider, Wong made early strides and led 10-5, but Kashyap clawed back at 11-11 and then zoomed ahead from 14-13 to 20-13 with a six-point burst. He then closed the door on the Malaysian.
Kashyap's next opponent is world number 22 Tien but the Indian will take heart from the fact that he had beaten him in the Macau Open in 2011.