Gasquet, ranked 15th in the world, dropped the first set but rallied for a 6-7 (7-9), 6-2, 6-2 victory over Lukas Rosol, advancing to the quarterfinals.
German player Michael Berrer advanced when his opponent, No. 3 seed Nicolas Almagro of Spain, retired with an injury to his right wrist. Berrer had won one set 7-5.
In other second-round matches, sixth-seeded Argentine Agustin Calleri defeated Pabro Cuevas of Uruguay 5-7, 7-5, 6-1, and Albert Montanes of Spain eliminated countryman Oscar Hernandez 7-6 (7-4), 6-4.
Simone Bolelli of Italy, seeded fifth, ousted German Mischa Zverev 6-7 (6-8), 6-4, 6-2, and Brian Dabul of Argentina topped Denis Gremelmayr of Germany 6-3, 5-7, 6-3, completing first-round matches that had been suspended Tuesday because of darkness.