Schwartzman, 26, mixed his game up to perfection to upset knock out Cilic 6-4, 6-4 as his preparations for Wimbledon received a major boost.
The Argentina Davis Cup star moved well across the court in a match lasting 83 minutes in west London.
Schwartzman opened a 3-1 lead in the opening set before Cilic levelled. However, Schwartzman raised his game a notch to take the set.
He stormed into a 2-0 lead in the second in a contest where he forced Cilic into 30 unforced errors.
A victorious Schwartzman is scheduled to meet fourth-seeded Russian Daniil Medvedev or Lucas Pouille of France in the last eight on Friday.
