Olympic bronze medallist Saina, who had clinched the Swiss Open in 2011 and 2012, saw off Germany's Karin Schnaase 21-7 21-15 in 33 minutes to set up a meeting with Czech's Kristina Gavnholt at St Jakobshalle here.
Sai Praneeth, who had stunned former World No. 1 Lee Chong Wei of Malaysia in the opening round of the All England Championship last week, prevailed over Uzbekistan's Artyom Savatyugin 21-7 21-10 in a 21-minute match.
In the opening round, eleventh seed Ajay Jayaram thrashed Malaysia's Jiann Shiarng Chiang 21-8 21-17. He will face Japan's Kenichi Tago next.
H S Prannoy, seeded 13th, also reached the second round after eking out a 21-19 21-19 win over Finland's Kalle Koljonen. The Indian will take on Germany's Lars Schaenzler in the next round.
Young Sameer Verma also continued to impress with a hard-fought 21-17 24-22 win over Denmark's Emil Holst. He will face the formidable Wang Zhengming of China in the next round.