Fils has advanced to the quarterfinals at three straight Masters following Indian Wells and Miami last month, and raised his record to 14-6 this season.
Two more seeded players were upset on Thursday.
Fourth-seeded Casper Ruud lost to Alexei Popyrin 6-4, 3-6, 7-5 and fifth-seeded Jack Draper was beaten by Alejandro Davidovich Fokina 6-3, 6-7 (6), 6-4. British left-hander Draper had service problems with 10 double faults and landed fewer than half of his first serves.
The 42nd-ranked Davidovich, who eliminated 11th-seeded American Ben Shelton in the first round, faces Popyrin in the quarterfinals.
Three-time Monte Carlo champion Stefanos Tsitsipas was playing the late match against unseeded Nuno Borges.
