The 20-year-old top seed, playing for the first time since a dramatic fourth-round French Open exit against Stan Wawrinka, was beaten 6-4, 3-6, 6-4 by the world number 60.
Jarry will next face either Kazakh Mikhail Kuskushkin or France's Richard Gasquet in the quarter-finals after his victory over world number six Tsitsipas.
Results from the 's-Hertogenbosch ATP/WTA tournament on Thursday (x denotes seeding):
Nicolás Jarry (CHI) bt Stefanos Tsitsipas (GRE x1) 6-4, 3-6, 6-4
David Goffin (BEL x5) bt Pierre-Hugues Herbert (FRA) 6-3, 7-5
Adrian Mannarino (FRA) bt Fernando Verdasco (ESP x4) 1-6, 6-3, 6-4
Christian Garín (CHI x7) bt Robin Haase (NED) 7-5, 7-5