Sindhu defeated Thailand's Porntip Buranaprasertsuk, seeded fifth, 23-21, 21-9 to set up a clash with fourth seed Nozomi Okuhara of Japan.
Jayaram saw off Malaysia's Daren Liew 21-16, 21-23, 21-8 and defeated compatriot Aditya Prakash 21-6, 17-21, 21-14 in the earlier round.
The 27-year-old Indian will take on Korea's Jeon Hyeok Jin on Saturday.
Commonwealth Games champion and third seed Parupalli Kashyap suffered a 21-13, 17-21, 13-21 loss to Zi Liang Derek Wong of Singapore in another men's singles match.
The 13th seeded B Sai Praneeth bowed out after suffering a 15-21, 17-21 loss to Lee Hyun Il of Korea.