Simon, the No. 2 seed, defeated Kenny De Schepper 6-2, 6-3. He won more points (29-28) off De Schepper's serve than De Schepper managed, and also had five breaks in moving into the quarterfinals.
Nicolas Mahut had a pair of breaks in each set of a 6-4, 6-4 upset of third-seeded Andreas Seppi and Carlos Berlocq advanced when No. 4-seeded Philipp Kohlschreiber, down 2-1 in the third set, retired.
Simon draws sixth-seeded Sam Querrey in Friday's quarterfinals, with a Becker-Mahut pairing also in that half of the draw. Top-seed and defending champion Jo-Wilfried Tsonga faces Tobias Kamke and Mayes goes against Berlocq in the other quarterfinals.