Defending champion Rafael Nadal has cruised to the last 16, while his fellow Spaniard and last year's finalist David Ferrer also booked his place in the fourth round of the 2014 French Open.
Nadal, an eight-time winner at the Roland Garros, defeated Argentina's Leonardo Mayer 6-2, 7-5, 6-2 to book his pre-quarterfinals berth.
After losing the first set easily, Mayer played much better in the second and broke Nadal's serve in the eighth game but the world number one quickly got the break back to avoid any comeback hopes of the Argentine and sealed the match in straight sets.
"It was a positive (first week)," Nadal said. "I have three matches that I think I played under control. That's always positive and good. Always (being in) the second week is great news, and winning in straight sets is a little bit better. I'm happy for that."
Meanwhile, Ferrer also faced little difficulty in overpowering Italian Andreas Seppi in the third round 6-2, 7-6 (2), 6-3. Seppi proved to be a no match for the fifth seed, who converted five break points and won 73 percent points on his first serve, on his way to a straight-set victory.
"I'm quite satisfied with the match," Ferrer said. "I would have liked to be more steady with my forehand and more consistent, but still, I'm happy."
"In the past five weeks I have started my matches in a more regular way, more consistent, I was more solid. I must say that as far as this is concerned, José (Altur - coach) has helped me a lot. We have worked a lot on this. That is how to kick off a match."
The Spaniard will next face Kevin Anderson, who has become the first South African since Wayne Ferreira in 1996 to reach the last 16 at the Roland Garros. Anderson was not made to work hard as his Croat opponent Ivo Karlovic retired due to a back injury.
19th seed Anderson was leading the match after winning the first set 6-3, when the 6ft 11in Karlovic retired only after spending 43 minutes on court.
Meanwhile, in the women's category, Russia's Svetlana Kuznetsova made a stunning comeback after losing the first set to beat fifth seed Czech Petra Kvitova 6-7 (3), 6-1, 9-7 in the third round. Both players exchanged blinding winners and absorbing rallies but it was Kuznetsova, who capitalised on countless errors committed by Kvitova.
"I knew I was going out there, and I was going to give everything I could and run every mile, every metre I could, and put as many balls back, try to be aggressive," Kuznetsova reflected. "Because if you watch the match, Petra was inside the court and I was next to the fans."
"I left out there everything I could. I come up with a win, but I was very close to the loss, as well. I was very strong mentally and really happy with that."