Djokovic, the world No. 1 and two-time tournament champion, doused Albert Montanes 6-2, 6-3 while winning about three-quarters of the points on serve. He won as many (28-28) points off Montanes' serve as Montanes managed.
Federer, seeded No. 2, routed Potito Starace 6-1, 6-2 in 50 minutes. Federer lost seven points in eight games serving, winning off his serve at an 82 percent clip. He also cashed in half of his eight break opportunities.
Kevin Anderson knocked off 11th-seeded Marin Cilic 6-3, 7-6 (9-7) for the only second-round upset Tuesday. Advancing to the third round were No. 6-seeded Tomas Berdych, who beat Denis Istomin 6-4, 6-0; seventh-seeded Juan Marin del Potro, who ousted Andrey Kuznetsov 6-3, 6-2; and No. 9-seeded Richard Gasquet, who defeated Grigor Dimitrov 6-4, 6-4.
No. 15-seeded Stanislas Wawrinka got by Carlos Berlocq 5-7, 6-3, 6-3 in a first-round match but Julien Benneteau eliminated 12th-seeded Nicolas Almagro 7-6 (7-2), 6-4 and Mikhail Youzhny handled 13th-seeded Tommy Haas 6-4, 6-3.
Florida bear attack: Black bear mauls woman's face
Toddler uninjured after being knocked over by Obama family dog