The twice grand slam champion, who has yet to win a title on clay, found little resistance as she avenged her defeat to Hsieh in Miami last month.
"If there is one positive thing I can say about myself, it's that I learn quickly," Osaka said. "So, for me it has been fun because I like to apply what I did wrong in the past, and I think that is what I was able to do today."
A break was enough for Osaka to win the first set as she looked somewhat uncomfortable on Stuttgart's quick indoor clay, designed to be similar to next month's French Open courts.
There was nothing wrong with her serve, however, as she fired seven aces during the contest.
After going 2-0 up in the second set, Osaka grew in confidence and broke again to seal her first win on clay this season on her first match point.
Victory also meant she will hold on to her world number one ranking after this week.
Osaka will next face Croatia's Donna Vekic who beat Daria Kasatkina 6-1 7-5.
World number five Angelique Kerber had little trouble in the all-German battle against wild card Andrea Petkovic, beating the former top-10 player 6-2 6-4.
She will play sixth seed Kiki Bertens who fired 20 aces as she battled back from a set down to beat Belinda Bencic 4-6 6-3 6-4.
Former world number one Victoria Azarenka of Belarus stunned fourth seed and defending champion Karolina Pliskova, needing two hours and 13 minutes to battle from a set down to win 4-6 6-3 6-4. She next takes on Estonian Anett Kontaveit.
(Reporting by Karolos Grohmann, editing by Pritha Sarkar and Toby Davis)
