Lyon loss hands Thiem fresh Roland Garros setback
Top seed Thiem, 27, lost to Britain's 49th-ranked Cameron Norrie 6-3, 6-2 in just over an hour.
Thiem, a two-time runner-up at Roland Garros, won just one match at the Italian Open last week, arriving in Rome on the back of a semi-final run at Madrid where he belatedly started his clay court season.
"It was an unexpected victory," said Norrie. "I played well and I could not be happier."
Norrie will face either French qualifier Arthur Rinderknech or Italian sixth seed Jannik Sinner for a place in the semi-finals.
Greek second seed Stefanos Tsitsipas, the champion at the Monte Carlo Masters, eased into the last eight against Tommy Paul of the United States 6-1, 6-4.
French number one Gael Monfils, who on Tuesday won a match for the first time in 15 months, was knocked out by Japan's world number 60 Yoshihito Nishioka, 4-6, 6-3, 7-6 (7/2).
Nishioka's reward is a clash with Tsitsipas on Friday.