Cilic, who skipped the U.S. Open warm-up tournaments in Montreal and Cincinnati due to injury, hit 80 unforced errors in an untidy display on Grandstand three years after he lifted the trophy at Flushing Meadows.
Schwartzman, seeded 29th after reaching the Rogers Cup final in Montreal, was overwhelmed in the opening set before finding his range to frustrate Cilic.
In a bottom half of a draw without a grand slam finalist and where American John Isner is now the highest seed at number 10, Schwartzman will take on either France's Lucas Pouille or Kazakh Mikhail Kukushkin for a quarter-final spot.
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(Reporting by Julien Pretot,; Editing by Ed Osmond)
