Spaniard Nadal swept aside Colombian qualifier Santiago Giraldo 6-3, 6-3 after Djokovic had survived a shaky second set in swirling winds on the Stadium court to beat Italian Andreas Seppi 6-3, 7-6.
Djokovic, who clinched his maiden Grand Slam title at the Australian Open in January, struggled for fluency after dominating his opponent with crunching groundstrokes before wrapping up victory in one hour and 40 minutes.
“Everybody could realise the wind was the most thing difficult today,” the 20-year-old Serb said in a courtside televised interview after clinching the tie-break 7-3.
Tenth-seeded Czech Tomas Berdych made an early exit, losing 2-6, 7-6, 6-4 to Swiss Stanislas Wawrinka.
In other matches, eighth-seeded Frenchman Richard Gasquet swept aside Swede Robin Soederling 6-3, 6-2 and Spaniard David Ferrer, the fifth seed, eased past Belgian Olivier Rochus 6-2, 6-2.
Jankovic wins
In the women’s event, erbia's world number four Jelena Jankovic and twice champion Lindsay Davenport coasted through their opening matches.
Jankovic, shrugging off strong winds, crushed American wildcard Ahsha Rolle 6-0, 6-2 and Davenport advanced when Argentina’s Gisela Dulko retired hurt with a thigh strain trailing 2-6.
However, world number two and top-seeded Serb Ana Ivanovic had to fight back after losing the second set before defeating Romania’s Ioana Raluca Olaru 6-1, 5-7, 6-0 in a match lasting one hour, 55 minutes. Earlier, sixth-seeded Marion Bartoli of France hammered Russia’s Elena Vesnina 6-0, 6-4 and Italy's Flavia Pennetta, the 19th seed, swept past Estonia’s Kaia Kanepi 6-2, 6-1.
Qualifier Evgeniya Rodina upset 16th-seeded Virginie Razzano 6-0, 6-7, 6-2 and another Russian-French pairing saw 12th seed Vera Zvonareva scrape past Aravane Rezai 6-3, 3-6, 6-3.
Sania through
Sania Mirza and her American partner Bethanie Mattek survived a tough test before securing their berth in the doubles quarterfinals. Sania and Mattek, seeded seventh, defeated Tatiana Poutchek of Belarus and Russian Anastasia Rodionova 6-2, 4-6, 10-7.
Sania will face her former doubles partner Shahar Peer in the third round of the singles after the ninth seeded Israeli prevailed over Uzbekistan’s Akgul Amanmuradova 6-1, 6-4.