Kashyap staved off the challenge of fourth seed Son Wan Ho of Korea, winning 21-15, 22-20, before Prannoy scripted another giant-killing act, sending Denmark's Jorgensen out of the tournament for the second time on the trot.
World No. 14 Prannoy, who had defeated Jorgensen at the India Super Series in New Delhi last month, beat the second seed 21-16, 21-8 to reach the quarter-finals. He had beaten the Dane at the Japan Open in 2013 as well.
Kashyap, who rose two places to world No. 15 in the rankings on Thursday, will next take on France's Brice Leverdez, who saw off another Dane, Hans-Kristian Vittinghun, 21-13, 19-21 21-18 in his pre-quarter-final match.
Prannoy will clash with world No. 10 Kento Momota of Japan on Friday.
However, it was a bad day in office for India’s world No. 4 Kidambi Srikanth, who lost 15-21, 20-22 to Thailand’s Tanongsak Saensomboonsuk.
The Delhi Commonwealth Games champion women’s doubles pair of Jwala Gutta and Ashwini Ponnappa also exited, beaten by third seeds Wang Xiaoli and Yu Yang of China 22-24, 18-21.
Image: H S Prannoy