Indian shuttlers make it through to the last eight in Lucknow
The 36-minute match was closely fought all the way, with things going Kashyap's way in the opening game. However, third-seeded Kidambi wrestled control from the two-time tournament winner over the next two games to book his place in Friday's quarterfinals with a 18-21, 22-20, 21-16 victory.
Srikanth will now face seventh-seeded Son Wan Ho of South Korea in the last eight.
Sourabh Verma also safely advanced, prevailing over fellow countryman Alap Mishra with a straight games victory.
Verma will now take on Thailand's Kunlavut Vitidsarn for a place in the semi finals.
Vitidsarn progressed from the second round after defeating top Indian shuttler Sai Praneeth in straight games 11-21, 17-21.
Number four seed Praneeth was always second best to his Thai opponent, and his fate was sealed after just over half an hour on court.
Also making his way out of the tournament was Ajay Jayaram. After losing the first game to China's Zhao Jun Peng, Jayaram rallied back to win the second and battled relentlessly in the third, securing eight match points before eventually losing out 18-21, 21-14, 28-30.
India's women's doubles duo of Ashwini Ponnappa and N. Sikki Reddy were also not spared misfortune on the day after they were forced to pull out of their match against the British pairing of Chloe Birch and Lauren Smith. Just a minute into the game, with the score at 0-2, Ponnappa suffered a leg injury that put her out of action.
Meanwhile, Carolina Marin kept up her positive comeback from a serious knee injury to outduel South Korea's Sim Yu Jin.
After losing the first game, the reigning Olympic gold-medallist fought her way back with a 19-21, 21-13, 21-11 victory and will face Russia's Evgeniya Kosetskaya on Friday.