Top seed Roger Federer begins against Colombia's Alejandro Falla, while Nadal plays Kei Nishikori of Japan.
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No. 3 David Ferrer won in straight-sets against Japan's Kei Nishikori, cruising to a 6-4 6-2 success.
France's Gilles Simon will face Japan's Kei Nishikori following a straight forward 7-5 6-3 win over Victor Hanescu.
The world No. 3 will next play Japan's Kei Nishikori, who he beat in last year's Australian Open quarterfinals.
Murray, the 2012 U.S. Open champion, will play Carlos Berlocq in the fourth round after the Argentine upset 16th seed Kei Nishikori.
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Japan's Kei Nishikori, the 17th seed also made the last 32 with a 6-2 6-2 6-4 win over home qualifier Tim Smyczek.
Meanwhile, defending men's champion Andy Murray reached the final of the ATP event in Brisbane as semifinal opponent Kei Nishikori of Japan pulled out injured in the second set.
The other quarterfinal will be between 21-year-old Canadian Milos Raonic, who beat fifth-seeded Czech Tomas Berdych, and Federer's Swiss compatriot Stanislas Wawrinka -- who defeated Japanese No. 14 Kei Nishikori.
But despite his near two-month absence from competition, the 31-year-old was back in the groove swiftly to set up a meeating with either Japan's Kei Nishikori or Viktor Troicki of Serbia.
In the men's ATP event, which is headed by Britain's Andy Murray, Japanese fifth seed Kei Nishikori began his campaign with a straights sets 7-5 6-2 win over Australian Marinko Matosevic.
He next plays No. 13-seeded Kei Nishikori, who became the first Japanese man in 75 years to reach the fourth round at Roland Garros, beating Benoit Paire 6-3, 6-7 (3), 6-4, 6-1.
Britain's Andy Murray , the sixth seed, beat Switzerland's Stanislas Wawrinka 6-1 6-3 6-3, and will next play Argentina's Juan Martin del Potro , who defeated Kei Nishikori of Japan 6-3 6-4 6-3.
No. 10 Nicolas Almagro and No. 16-ranked Kei Nishikori also moved on while No. 24 Jerzy Janowicz of Poland rallied from two sets down to overpower India's Somdev Devvarman 6-7 (10), 3-6, 6-1, 6-0, 7-5.
He is scheduled to play his fourth-round match against 16th-seeded Philipp Kohlschreiber of Germany on Monday, when seven-time French Open champion Rafael Nadal hopes to celebrate his 27th birthday with a win against 13th-seeded Kei Nishikori.
Federer, whose return to action in Madrid after a two-month break ended with a third-round loss to Japan's Kei Nishikori, also eased through to the third round after beating Italian wild card Potito Starace 6-1 6-2.
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Other players left sitting it out were third seed Tomas Berdych of the Czech Republic, who was due to play home hope Tommy Robredo, fifth seed Milos Raonic of Canada and Japan's sixth seed Kei Nishikori.
Japan's Kei Nishikori reached the last eight thanks to a 6-3 6-3 win over Spain's Tommy Robredo, while Alexandr Dolgopolov of Ukraine progressed when Finland's Jarkko Nieminen retired due to a migraine with the Ukrainian ahead 6-2 4-1.
Djokovic, seeking his fourth Miami crown, having also won in 2007 as well as losing the 2009 final, was joined in the last 16 by Spanish third seed David Ferrer, who will next play Japan's No. 13 Kei Nishikori.
Bidding to become the first man in tennis history to win eight titles at the same major championship, Nadal won 6-4 6-1 6-3 against 13th seed Kei Nishikori, the first Japanese man in the fourth round since Fumiteru Nakano in 1938.
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