World number 2 Djokovic defeated Portugal's Joao Sousa in straight sets 6-1 6-4 6-3 to advance. Tournament favourite Nadal too won in straight sets producing identical scoreline as Djokovic. He defeated Netherland Robin Hasse.
Rafael Nadal confidently moved one step closer to a potential 10th French Open title with a 6-1, 6-4, 6-3 second-round victory over Robin Haase.
The Spaniard needed just an hour and 49 minutes on Wednesday to overcome his 46th-ranked opponent, playing a clean match in which he struck 33 winners, committed just 13 unforced errors and did not face a single break point, Efe news reported.
The world No. 4 rolled through one service game after another in his first match this year in the French Open's main stadium, Philippe-Chatrier Court, remarkably winning an even higher percentage of second-serve points (85 per cent) than first-serve points (76 per cent).
The Dutchman settled down and was more competitive after a lopsided first set but never posed a serious threat to Nadal, winner of a record nine Roland Garros men's singles titles.
"I think I played a good match. No, no, I can't say another thing. I think I played a solid match. Hitting very well the ball with the forehand. I think my serve worked better than two days ago," Nadal said in the post-match press conference.
The 30-year-old Spaniard, who is trying to win the French Open for the first time since 2014, sustained a wrist injury last year that forced him to withdraw from the event prior to his third-round match.
But he said that the injury had not resurfaced in 2017.
"I don't feel anything on the wrist since long time ago. Treatment went well so I've had no wrong feeling since the beginning of the season with the wrist. That's good news."
Next up for the Spaniard in the third round will be 63rd-ranked Georgian Nikoloz Basilashvili, who edged Serbian Viktor Troicki 7-6 (7-3), 7-6 (7-2), 7-6 (8-6) on Wednesday.
In another important clash, 11th seeded Gregor Dimitrov defeated veteran Spanish player Tommy Robredo in straight sets 6-3, 6-4. 7-5.