World number 52 Sugita took his chances to break his seventh-ranked opponent three times, before clinching one of the biggest wins of his career in just under an hour and a half.
The result represents a setback for Thiem's Wimbledon preparations, with the Austrian having failed to progress beyond the last-16 in his four appearances at the All England Club.
Earlier in the day at Halle, big-hitting Russian Karen Khachanov overcame Japan's Kei Nishikori for the second straight year at the last-16 stage.
The 22-year-old Khachanov fired seven aces and broke his opponent's serve twice in each set to win 6-2 6-2 in 78 minutes.
"I had to play more aggressive," Khachanov, recording his 20th match win of the season, said courtside.
"I had good memories here on centre court. I played three matches here last year so it gave me a lot of confidence and experience. This year has been great so far."
Khachanov will next face Spanish fourth seed Roberto Bautista Agut, who overcame Dutchman Robin Haase 6-4 7-5.
(Reporting by Hardik Vyas in Bengaluru; editing by John Stonestreet)
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