Djokovic, the world No. 1, posted a 6-1, 7-6 (7-4) decision over Roberto Bautista-Agut. Djokovic won the first four games of the match and then had a string of five straight for a one-set, 3-0 lead.
Bautista-Agut stubbornly fought back, getting his first break of the game to pull even in the second set at 5-5. Djokovic, however, won three straight points for a 5-2 lead in the tiebreaker and Bautista-Agut had a double fault at match point.
Federer took out Marcel Granollers 6-3, 6-4, saving all three break points he saw in the process. He lost only 18 points in 10 games -- six over five games in the first set -- serving and used a break in each set to advance.
No. 3-seeded Tomas Berdych handled Tobias Kamke 7-5, 6-1, despite having to deal with 14 break points, while fourth-seeded Juan Martin del Potro took out Smote Defaming 6-4, 6-4 without dropping serve.
Seventh-seeded Andreas Sepia was a 6-4, 7-6 (7-4) winner over Lukas Rosily but Daniel Brands posted a 6-4, 6-4 upset of eighth-seeded Mikhail Huzzahing.
Also Wednesday, which saw the entire second round contested, Dmitry Turgenev beat Michael Leodora 7-6 (7-5), 2-6, 6-3 and Niko lay Davydenko stopped Victor Haynes 6-4, 7-6 (7-2).