Gasquet, the No. 2 seed in the event, stopped Paolo Lorenzi 6-1, 6-1. He lost 12 points over seven games serving and won 61 percent of the points off Lorenzi's serve. He turned back the only break point he faced.
Third-seeded Stanislas Wawrinka also advanced to the quarterfinals as he defeated Ivan Navarro 7-6 (7-5), 6-1. Wawrinka limited Navarro to nine points in the second set.
No. 6-seeded Robin Haase claimed a 5-7, 6-4, 6-2 decision over Inigo Cervantes, getting two breaks in each of the second and third sets.
Wawrinka is paired against Haase and Gasquet is to take on Munoz-de la Nava in the quarterfinals.