French Open runner-up Thiem double-faulted four times and landed only 53 percent of his first serves in play as he struggled to find his rhythm on the German grass.
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.
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.
Khachanov will next face Spanish fourth seed Roberto Bautista Agut, who overcame Dutchman Robin Haase 6-4 7-5.
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