Nadal continued his ruthless form at Roland Garros by dispatching Spanish 17th seed Roberto Bautista Agut 6-1, 6-2, 6-2 to match Roger Federer's mark of last-eight appearances in Paris.
The 14-time major winner is yet to drop a set, conceding just six games in the last two rounds as he strives to become the first man to win 10 titles at a single Grand Slam.
"I'm happy because Roberto is a very good player. It's very important for me to be in the quarter-finals one more time," said Nadal, who turned 31 on Saturday.
Japan's Kei Nishikori fought off a fierce five-set challenge from rising South Korean talent Hyeon Chung to clinch a place in the last 16.
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Eighth seed Nishikori led two sets to one but trailed by a double break at 3-0 down in the fourth set when rain halted play on Saturday.
Chung forced the contest into a deciding set as play resumed on Sunday, but the world number 67 double faulted on match point to gift Nishikori a 7-5, 6-4, 6-7 (4/7), 0-6, 6-4 victory.
"I knew I had to change something to beat him today, so I think I made some adjustments to make little better than yesterday."
- 'Second chance' -
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It was the first third-round meeting between two Asian players at Roland Garros, with 2014 US Open finalist Nishikori going on to play Fernando Verdasco for a place in the quarter-finals.
Karen Khachanov will play Andy Murray in the fourth round after the giant Russian beat American 21st seed John Isner 7-6 (7/1), 6-3, 6-7 (5/7), 7-6 (7/3).
Wozniacki, who made her only other last-eight appearance at Roland Garros in 2010, will meet either Australia's Samantha Stosur or Jelena Ostapenko of Latvia for a semi-final place.
"Svetlana's a great player, especially on clay so I knew it wouldn't be easy," said Wozniacki, a two-time US Open runner-up.
Second seed Karolina Pliskova advanced to round four with a 7-5, 6-1 victory over Germany's Carina Witthoeft.
Pliskova, who had won just twice in five previous French Open appearances before this year, will face Paraguay's Veronica Cepede Royg for a quarter-final spot.
Croatia's Martic, a former top 50 player whose ranking slumped after a back injury sidelined her for 10 months, will face Ukraine's Elina Svitolina.
"When I got injured, my only hope was that I would get a second chance so I can play some of my best tennis again," said Martic.
"I still can't believe that I'm sitting here."
Fifth seed Svitolina downed Magda Linette of Poland 6-4, 7-5.
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