Djokovic, the world No. 1, defeated Paul-Henri Mathieu 6-2, 6-4, 7-5 by winning 81 percent of the points on serve. Djokovic lost only 15 points while serving and saved the three break points he faced.
Mathieu won nearly two-thirds of the points on serve but Djokovic finished off four of his seven break chances in advancing.
Marcos Baghdatis, the No. 28 seed, eked out a 6-7 (0-7), 7-6 (7-4), 6-4, 3-6, 6-3 win over Alberto Ramos in 4 hours, 15 minutes. It was one of 10 matches that went five sets.
One of those lengthy matches was 10th-seeded Nicolas Almagro's 7-5, 6-7 (4-7), 6-2, 6-7 (6-8), 6-2 win over Steve Johnson. Other seeded winners included 15th-seeded Stanislas Wawrinka and No. 16 Kei Nishikori.
Andrey Kuznetsov upset 11th-seeed Juan Monaco 7-6 (7-3), 6-1, 6-1, winning nearly two-thirds of the points over the last two sets.
Other seeded first-day winners were: 20th-seeded Sam Querrey, No. 22 Fernando Verdasco, 23rd-seeded Mikhail Youzhny, No. 24 Jerzy Janowicz, No. 26 Jurgen Melzer; 31st-seeded Radek Stepanek and No. 32 Julien Benneteau.
Unseeded players advancing included: Kevin Anderson, Tatsuma Ito, Carlos Berlocq, Roberto Bautista Agut, Ryan Harrison, Evgeny Donskoy, Somdev Devvarman, Lukas Lacko, Edouard Roger-Vasselin, Feliciano Lopez, Guillaume Rufin, Xavier Malisse, Tim Smyczek, Brian Baker, Daniel Gimeno-Traver and Tobias Kamke.