Maria Sharapova helped restore order at the French Open on Saturday following the shock exits of the top two seeds Caroline Wozniacki and Kim Clijsters.
The seventh seeded Russian comfortably reached the last 16 with a 6-2 6-3 win over Taiwan qualifier Chan Yung-Jan.
Poland's Agnieszka Radwanska, 12th seed, eased past Belgium's Yanina Wickmayer 6-4 6-4 to set up a clash with Sharapova.
Fourth seed Victoria Azarenka swept aside Roberta Vinci 6-3 6-2.
The 21-year-old from Belarus wrapped up her win in 66 minutes and will next play Russia's Ekaterina Makarova who beat 16th seed Kaia Kanepi 6-4 7-5.
The leading seeds have been falling fast in the women's draw during the first week.
Defeats for Clijsters and then Wozniacki on Thursday and Friday means this is the first Grand Slam since the Open era began in 1968 in which the top two women's seeds have failed to reach the fourth round.
Third seed Vera Zvonareva is still involved, but she had to survive a scare - and a match-point - in her second-round match against Sabine Lisicki on Wednesday, meaning Azarenka has been by far the most convicing member of the world's top four during her progress in Paris.
She has only dropped a total of 12 games in her three matches to date, although the variety of Vinci's play did give her a few problems at the end of the first set.
Azarenka faltered when she served for the set at 5-1 but made no mistake at her next opportunity, sealing it with one of her trademark thumping forehands.
Vinci was broken again at the start of the second set and a barrage of groundstrokes from Azarenka meant the 30th seed was unable to change the momentum of the match.
Despite her comfortable progression, Azarenka said: "I think I can improve, and I have been improving from match to match, which is important. I probably could do things better, but I have time to work on and prepare for the next match."
Sixth seed Li Na made easy progress, seeing off Romania's Sorana Cirstea 6-2 6-2, in only 61 minutes.
Cirstea, who reached the 2009 quarter-finals in Paris, had her serve constantly pressured by Li and the Chinese woman remained in control throughout as she booked her place in the fourth round at Roland Garros for only the second time.
Na will play ninth seed Petra Kvitova next, after the Czech beat Elena Baltacha's conqueror Vania King 6-4 6-2.