Kerber, the world number one who crashed out of last week's China Open in the round of 16 at the hands of Elina Svitolina, made five double faults but saved eight of 10 break points against world number 97 Sakkari.
"I had never played my opponent and that makes it tough," Kerber told reporters. "It will be the same in my next match. But in the end I have to focus on my game."
The German will face American Louisa Chirico in the next round.
Fifth seed Caroline Wozniacki of Denmark beat China's Zheng Saisai 6-1 6-4 to set up a second-round clash with Britain's Heather Watson who is seeded ninth and beat New Zealand's Marina Erakovic 7-5 7-6(9).
Defending champion Jelena Jankovic of Serbia beat American Samantha Crawford 6-3 6-1.
Stosur completed a hat-trick of first-round exits following her defeats at the China and Wuhan Opens as she was well beaten by Hibino who is ranked 84th in the world.
(Reporting by Simon Jennings in Bengalaru, editing by Ed Osmond)
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