Tsitsipas was playing his first match since losing to Stan Wawrinka in the last last-16 of the French Ope.
The 20-year-old will look to improve on last year's fourth-round appearance at Wimbledon when he returns to the All England Club next month.
Jarry will meet either Kazakh Mikhail Kukushkin or France's Richard Gasquet in Friday's quarter-finals.
(Reporting by Hardik Vyas in Bengaluru; editing by John Stonestreet)
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