Gasquet, Wawrinka move on in Estoril
Former finalist Gasquet secured a comprehensive 6-1 6-1 win over Paolo Lorenzi in his first clay court match of the season.
Gasquet will next play qualifier Daniel Munoz-De La Nava for a place in the last four.
Wawrinka defeated Spanish qualifier Ivan Navarro 7-6(5) 6-1 in his first appearance at the Portuguese venue. He will next face sixth-seeded Dutchman Robin Haase.
Argentine Juan Martin Del Potro is the tournament's top seed.