The top-seeded Indians had contrasting straight-game victories in their first-round matches.
While Kidambi eased to a 21-12, 21-11 victory over Russian Vladimir Malkov, Praneeth had to dig deep for his 21-16, 22-20 win against Malaysian Iskandar Zulkarnain.
Carolina Marin, who was playing in India for the first time since suffering a serious knee injury earlier in the season, also advanced after defeating Bulgaria's Linda Zetchiri.
While the top-seeded Indians made it to the next round, the third-highest seed, Sameer Verma fell in three games against Ajay Jayaram.
All was seemingly going to plan for the 25-year-old after he won the first game 21-15, but after losing a hard-fought second game 18-21, Verma lost all momentum and ended up surrendering the third game 13-21, handing Jayaram the win.
Top-seed Shi Yu Qi also suffered a surprise exit from the first-round after being beaten 25-23, 21-17 by Malaysian Soo Tech Zhi.
Over in the women’s doubles, Ashwini Ponnappa and N. Sikki Reddy fought hard and beat Hong Kong’s Ng Tsz Yau and Yuen Sin Ying 21-13, 16-21, 21-19 to advance to the second round. However, the men’s doubles second-seeded duo of Satwiksairaj Rankireddy and Chirag Shetty succumbed to a straight-games loss against Chinese pair Di Zi Jian and Wang Chang.
The Chinese team dominated the first game and won it 21-12 in emphatic fashion. The Indian pair raced to a 7-3 lead in the second and seemed to have found their rhythm, but Di and Wang were relentless on the day and levelled the game at 7-apiece.
The game remained evenly contested the rest of the way, with neither team successfully pulling away on the scoreboard. Then, with the score pegged at 20-20, Rankireddy and Shetty got the all-important edge that gave them game point, but three unanswered points from the Chinese duo eliminated the Indian pair from the tournament.
It took just 32 minutes for the Spaniard to wrap up victory and move through to a second round tie with South Korea's Sim Yu Jin.
Marin to withdraw in the first round of the Gwangju Korea Masters last week after suffering from an unspecified sickness.
The Syed Modi International has also seen a number of players pull out, including reigning world champion PV Sindhu and London 2012 bronze medallist Saina Nehwal.
Nehwal announced that she would not take part earlier in the week, after a season blighted by injury and illness.
Parupalli Kashyap and Lakshya Sen were handed walkovers and the two are scheduled to be in second-round action tomorrow.