Cilic, the top seed, beat Germany's Daniel Brands 7-6 (9-7), 6-4. Simon, the third-seed, topped Jan Hajek of the Czech Republic 6-1, 2-6, 6-4.
Cilic hit seven aces and won 79 percent of his service points. Monfils, No. 15 in the latest men's world rankings, won in about 90 minutes, improving his record this season to 37-16.
Sixth-seeded Feliciano Lopez of Spain downed Austria's Daniel Koellerer 6-3, 6-3; seventh-seeded Jurgen Melzer of Austria beat Slovakia's Dominik Hrbaty 6-4 7-5; and Serbia's Janko Tipsarevic was a 7-6 (7-3), 6-1 winner over German Michael Berrer.
Friday's quarterfinals are Cilic-Lopez; Melzer-second-seeded Radek Stepanek; Monfils-Tipsarevic; and Philipp Kohlschreiber-Nicolas Almagro.
Celebrity Families of 2014 [PHOTOS]