Top-seeded Jo-Wilfried Tsonga of France edged Thomaz Bellucci of Brazil 6-3, 7-6 (7-3) and will face qualifier Sergiy Stakhovsky in the third round.
Stakhovsky cruised past No. 15 seed Pablo Andujar of Spain Tuesday 6-2, 6-3.
Second-seeded Tomas Berdych of the Czech Republic upended Russia's Alex Bogomolov 6-3, 7-5, and No. 3 seed and defending champion John Isner of the United States needed three sets to eliminate Martin Klizan of Slovakia 4-6, 6-3, 7-5.
Other winners Tuesday included fourth-seeded Alexandr Dolgopolov and sixth-seeded Marcel Granollers of Spain.
Eighth-seeded Julien Benneteau of France lost to Lukasz Kubot 2-6, 7-5, 6-3. No. 12 seed Kevin Anderson of South Africa fell to Ernests Gulbis of Latvia 6-4, 7-6 (7-2).