While 2012 London Olympics bronze medallist Saina was made to work hard for her 12-21, 21-10, 21-12 win over Germany's Karin Schnaase, two-time World Championships bronze medallist P.V. Sindhu registered a 21-12, 22-20 victory over Hong Kong's Pui Yin Yip at the Odense Sports Park.
Saina got off to a poor start in the first game, losing 12-21 before showing her class to win the second game 21-10 and continued to pressurise Karin with her regal smashes.
The World No.7 wrapped up the third game 21-12.
In the other match, Sindhu was in her element from the start as she didn't allow Yin Yip to settle down.
The World No.10 Indian won the first game 21-12 before her opponent got some rhythm going in the second game.
Sindhu won the closely-fought second 22-20 to reach the next round.
Earlier in the day, the Indo-Russian mixed doubles pair of Ashwini Ponnappa and Vladimir Ivanov were knocked out in the first round, losing 18-21, 18-21 in 30 minutes to Hong Kong pair Yun Lung Chan and Ying Suet Tse.
The Indo-Russian team fought hard during the match but failed to get the better of Chan-Tse, who took advantage of small mistakes made by Ponnappa and Ivanov.