The two-time Roland Garros runner-up Djokovic got past veteran Finnish left-hander Jarkko Nieminen 6-2, 7-5, 6-2, while the former world No. 1 great Nadal eased past 296th-ranked Frenchman Quentin Halys 6-3, 6-3, 6-4 on Court Chatrier. Djokovic trailed 2-5 in the second set before charging back to win 11-of-13 games against Nieminen and extend his current winning streak to 23 matches.
Djokovic surged to a 4-0 lead in the third set, before Nieminen made life difficult for the top seed. The 33-year-old Finn saved three match points in a 14-point seventh game. Djokovic eventually closed out on his fifth match point and is now 36-2 on a season, including five titles.
Nieminen is now 0-11 against world No. 1s.
The 14-time Grand Slam champion Nadal beat the eight-time major titlist Djokovic in last year's final to capture a fifth straight title at Roland Garros, where the Spanish star is now 67-1 for his career, including a victory over Djokovic in the 2012 final as well.
Nadal entered this fortnight with his lowest seed ever in Paris -- No. 6. He did not win any of the four French Open tune-up events this spring, including a loss to Andy Murray in a Masters final in Madrid.
Nadal will face fellow Spaniard Nicolas Almagro in the round of 64.
Ferrer, the seventh seed and 2013 French Open runner-up, blasted Slovakia's Lukas Lacko 6-1, 6-3, 6-1, while Cilic, the ninth seed and reigning U.S. Open champ, had little trouble in a 6-2, 6-4, 6-2 romp of Dutchman Robin Haase.
Also on Day 3, 15th-seeded South African Kevin Anderson handled American Tim Smyczek 6-4, 6-4, 6-2, 20th-seeded French favorite Richard Gasquet rolled past Belgian Germain Gigounon 6-3, 6-4, 6-0 and 23rd-seeded Argentine Leonardo Mayer outlasted Czech Jiri Vesely 3-6, 7-6 (8-6), 6-3, 5-7, 6-2. Mayer was a runner-up on clay in Nice last week.