London Olympics bronze medallist Saina staved off a spirited challenge from World No. 44 Mette Poulsen of Denmark before emerging 21-19 23-21 winner in a 46-minute match.
World No. 11 Saina, who won the bronze at the World Championship, will next face a tough opponent in eighth seeded Chinese Chen Yufei, who had clinched the other bronze at the Glasgow Worlds in August.
Olympic silver medallist Sindhu, seeded second, disposed off Hong Kong's Leung Yuet Yee 21-18 21-10 to set up a clash with either Japan's Aya Ohori or Russia's Evgeniya Kosetskaya in the next round.
In men's singles competition, Prannoy survived a scare against Hong Kong's Hu Yun to win 19-21 21-17 21-15 in a match that lasted a little over an hour.
The World No. 10 Indian will face Japan's Kazumasa Sakai, who had defeated the Indian in the semifinals of Indonesia Open Super Series Premier.
However, Commonwealth Games champion Parupalli Kashyap squandered an opening game advantage to go down narrowly 21-15 9-21 20-22 to Korean Lee Dong Keun, while Sourabh Verma failed to put up a fight against Indonesia's Tommy Sugiarto, losing 15-21 8-21 to bow out of the competition.
B Sai Praneeth also lost his first round match against second seeded Son Wan Ho of Korea 8-21, 16-21. Women's doubles pair of Ashwini Ponnappa and N Sikki Reddy played their hearts out before going down 11-21 21-19 19 -21 against the Chinese combo of Huang Dongping and Li Wenmei in a hard-fought contest.
The mixed doubles pair of Manu Attri and B Sumeeth Reddy went down fighting to the pair of Khim Wah Lim of Malaysia and Yoo Yeon Seong of Korea 17-21, 17-21 in the opening round.
Prannoy lagged behind for most part of the opening game even though he did manage to turn the tables a few times, taking slender leads at 9-8, 13-12 and 16-15. But Hu Yun managed to keep his nose ahead to pocket the first game.
The Indian, however, produced a better performance in the second as he fought back from 0-5 down to lead 11-8 at the break and then surged ahead, despite some tough fight from the local hero.
In the decider, Hu Yun once again jumped to a 5-0 lead but Prannoy narrowed the deficit to 10-11 at the breath. Hu managed to grab a 14-12 advantage but the Indian reeled off eight straight points to move to the match point. Hu saved one before Prannoy sealed it without much ado.
(With inputs from PTI)