Nadal, who next faces Russian Teymuraz Gabashvili or Argentine Leonardo Mayer, is on a quarter-final collision course with last years runner-up and compatriot David Ferrer.
Fifth seed Ferrer, one of three men to beat Nadal on clay this season, wasted little time in demolishing Italian Simone Bolelli 6-2 6-3 6-2.
I am ready for the next round and was very happy with my performance, especially with my consistency, he said. My season on clay has been good. I have a good feel. Im focusing on the moment.
Murray at ease
Andy Murray looked at ease on court as he disposed of Australias Marinko Matosevic 6-3 6-1 6-3 to reach the third round with some dazzling tennis. Matosevic, playing in the second round of a grand slam tournament for only the second time after 12 first-round exits in a row, occasionally produced some fireworks but Murray was a class apart, losing serve just once when he served for the match after which he broke back to love.
Murray also found himself 40-0 down on serve in the middle of the first set but Matosevic could not convert any of his three chances and was never close to his opponent again. Next up is Germanys Philipp Kohlschreiber, a player he has lost to before on clay.
Tough, very tough match for me, Murray, who missed the 2013 French Open with a back injury, said. I played him once before on clay and I think I got three games or something.
In the absence of the Williams sisters, 15th seed Sloane Stephens raised American morale by easing past Slovenian Polona Hercog 6-1 6-3 to reach the third round. Stephens followed her teenage compatriot Taylor Townsend, who on Wednesday became the youngest player to go past the second round at Roland Garros since 2009 on the day world No.1 Serena Williams and her elder sister Venus were knocked out.
The 21-year-old Stephens blazed through the opening set before running into a spot of bother midway through the second as Hercog upped her game but the American ended the contest on her second match point with a crosscourt forehand winner.
Sixth seed Jelena Jankovic proved strong on serve to hold off Japanese Kurumi Nara, who collapsed in the second set in a 7-5 6-0 defeat by the Serbian who is a three-times semi-finalist in Paris.
It was not easy, she is returning a lot of balls and the court is heavy and the conditions generally are heavy, Jankovic said. Every round is going to be tough.
Former French Open champion Ana Ivanovic of Serbia reached the third round by beating Elina Svitolina of Ukraine 7-5, 6-2. The 11th-seeded Ivanovic dropped her own serve three times but broke Svitolinas serve six times. She clinched victory on her second match point with a forehand winner down the line on Svitolinas serve. She next faces No. 23 Lucie Safarova of the Czech Republic, who won 6-1, 5-7, 6-3 against Casey Dellacqua of Australia.
Fifth seeds Sania Mirza and Cara Black breezed past their first round opponents while Rohan Bopanna and Aisam-Ul-Haq Qureshi were shown the door.
The Indo-Zimbabwean pair of Mirza and Black began their womens doubles campaign with a 6-3, 6-3 win over Slovakias Daniela Hantuchova and Israels Shahar Peer on Court 11. They will next play the Canadian-Polish combine of Gabriela Dabrowski and Alicja Rosolska. Bopanna and his Pakistani partner Qureshi, however, suffered a 3-6, 4-6 loss at the hands of unseeded Jonathan Erlich and Marcelo Melo.
results (round 2): Mens Singles: Rafa Nadal (1) def. Dominic Thiem 6-2, 6-2, 6-3; David Ferrer (5) def. Simone Bolelli 6-2, 6-3, 6-2; Andy Murray (7) def. Marinko Matosevic 6-3 6-1 6-3.
Womens Singles: Simona Halep (4) def. Heather Watson 6-2, 6-4; Petra Kvitova (5) def. Marina Erakovic 6-4, 6-4; Jelena Jankovic (6) def. Kurumi Nara 7-5, 6-0; Sara Errani (10) def. Dinah Pfizenmaier 6-2, 6-4.