Seventh seed Anand easily overcame the challenge of Chinese Taipei's Jen Hao Hsu, winning 21-10, 21-14 in 30 minutes, while 10th seed Bhatt scraped past compatriot RMV Gurusaidatt 21-16, 18-21, 21-15 in a 53-minute second round contest.
However, P Kashyap, Sayali Gokhale, Aditi Mutatkar fell by the wayside.
Kashyap, seeded 14th, squandered a game's lead and went down 17-21, 21-17, 21-11 to China's Huan Gao in a men's singles second round clash that lasted 70 minutes.