The fifth-seeded Saina was made to work hard by Kirsty Gilmour of Scotland in her 21-19 21-16 win in the second round of the women's singles.
Saina, who took just 37 minutes to outplay local girl Sashina Vignes Wara in the opening round, outplayed Kirsty in 39 minutes.
Commonwealth Games gold medallist Parupalli Kashyap also had it tough against China's Houwei Tian 21-19 21-18 to make it to the third round.
In mixed doubles, Ponnappa and Ivanov got past the Chinese pair of Lu Kai and Huang Yaqiong 21-8 18-21 21-9 in the second round.
The Indo-Russian pair of Ponnappa and Ivanov also took 39 minutes to dispatch their seventh-seeded opponents.
The Ponappa-Ivanov duo had got the better of Keigo Sonoda and Shizuka Matsuo of Japan in the first round match.