US and Australian Open champion Osaka, who lost to Taiwanese veteran Hsieh in Miami last month, secured a place in the quarter-finals against Croatia's Donna Vekic as she launched her preparations for Roland Garros.
The Japanese star arrived in Stuttgart, where she last played as a qualifier in 2017, after suffering early exits in her last three tournaments.
Osaka has admitted the difficulty of dealing with the trappings of fame and becoming the world's top player in recent months, a period which saw her split with coach Sascha Bajin after the Australian Open.
"I am really grateful for everyone that has been really positive towards me. It was really rough the last couple of months. The kid was depressed out there."
"If there is one positive thing that I can say about myself, it is that I learn quickly," said Osaka, who reached the last eight of a tournament for the first time since her coaching split.
"Definitely I've put a lot on pressure on myself and found it hard to deal with in the first few tournaments.
"Now I start trying to have fun out there, which is what I did before I was number one."
Osaka, 21, broke Hsieh three times in total to beat the Taiwanese for the second time in three attempts this year, having also defeated her on the way to lifting the title in Melbourne.
"I did feel like I am in control, but I also felt she is taking more risks than me," said Osaka.
- 'Tricky opponent' -
"She's a really tricky opponent. You never really know what she's going to do."
Osaka needed 84 minutes to dispatch the unconventional Hsieh, ensuring she will hold on to top spot in the rankings for at least another week.
She is less than 200 points ahead of Simona Halep in the WTA rankings, although the Romanian pulled out of this week's tournament with a hip injury.
Top seed Osaka hit 22 winners and just 16 unforced errors.
Osaka will meet Vekic, a 6-1, 7-5 winner over Daria Kasatkina, for a spot in the last four, while Latvian seventh seed Anastasija Sevastova defeated 2017 champion Laura Siegemund 6-4, 6-3.
Sevastova will meet third-ranked Petra Kvitova next.
German number one Angelique Kerber, who won in Stuttgart in 2015 and 2016, put away good friend Andrea Petkovic on her fourth match point to progress 6-2, 6-4.
Estonia's Anett Kontaveit eased past Anastasia Pavlyuchenkova 6-3, 6-2, while Dutchwoman Kiki Bertens took down Belinda Bencic 4-6, 6-3, 6-4.
Defending champion Karolina Pliskova was later knocked out by former world number one Victoria Azarenka.
Two-time major winner Azarenka battled back to beat the fourth-seeded Czech 4-6, 6-3, 6-4 and next faces Kontaveit.