Federer saved a break point in the third and fifth games of the first set. In the second set, the top-ranked Federer went up 3-0 up and had eight break points in the fourth game, but Bracciali managed to hold after 11 deuces.
The Swiss star will next face seventh-seeded Novak Djokovic of Serbia, who beat Rainer Schuettler of Germany 7-6 (5), 6-3.
Olivier Rochus of Belgium upset third-seeded Nikolay Davydenko of Russia 4-6, 6-4, 6-2, and Mikhail Youzhny of Russia topped sixth-seeded Tomas Berdych of the Czech Republic 7-6 (6), 6-3.
Fifth-seeded Tommy Haas of Germany beat Florent Serra of France 7-6 (5), 6-3.