Eighth-seeded Tomas Berdych of the Czech Republic also advanced, beating Gael Monfils of France 6-3, 6-2.
The 26-year-old will now face Tomas Berdych in his eighth consecutive semifinal at Indian Wells.
France's Richard Gasquet will play Andy Murray after seeing off 13th seed Tomas Berdych 6-4 6-1.
In the other semifinal, Russian qualifier Dmitry Tursonov will face top seed Tomas Berdych.
Meanwhile, sixth seed Tomas Berdych sealed a quarterfinal place with a 7-6 7-5 win over Kevin Anderson.
Murray will now face either Frenchman Richard Gasquet or Czech fourth seed Tomas Berdych in the semi-finals.
Sam Querrey lasted only 50 minutes in the fourth round and lost to Tomas Berdych, 6-1, 6-1.
Third seed Tomas Berdych moved into the third round, with the Czech defeating Spain's Pere Riba 7-5 6-1.
The Swede will now meet Tomas Berdych after the Czech giant-killer battled back to see off Fernando Verdasco.
Czech 16th seed Tomas Berdych, who knocked out Federer on Wednesday, will play Spanish No. 10 Fernando Verdasco.
Tomas Berdych set up a third-round match with Verdasco after beating Richard Gasquet of France in straight sets.
Spaniard Robredo, the fifth seed, lost 1-6 6-3 6-2 to 10th seed Tomas Berdych of the Czech Republic.
Tomas Berdych beat Jiri Novak in straight sets to advance while Belgian Kristof Vliegen upset compatriot Christophe Rochus.
Put Nadal on a wet clay court with Djokovic or even Gulbis, Roger Federer, or Tomas Berdych and he could suffer.
He fought from behind in the quarter finals against Marin Cilic and the semis against Tomas Berdych.
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Fifth seed Tomas Berdych lost to German Mischa Zverev 3-6 6-2 7-6 (10-8).
He will play either world No. 5 David Ferrer or Czech Davis Cup winner Tomas Berdych on the second day.
In the semifinals he will play Latvian Ernests Gulbis, who enjoyed a 3-6 6-3 7-6 win over fifth seed Tomas Berdych.
Elsewhere, Tomas Berdych , the No. 7 seed looked in good touch as he dispatched France's Michael Llodra 6-2 6-3 6-3.
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Spaniard Nadal, the second seed in Monaco, defeated 10th seed Tomas Berdych of the Czech Republic 6-0 7-5 in Saturday's semi-finals.
The BMW Open title in Munich went to Czech Tomas Berdych who edged out Mikhail Youzhny of Russia 6-4 4-6 7-6.
The Russian will next face world No. 45 Philipp Petzschner, who upset defending champion and third seed Tomas Berdych 1-6 6-3 6-4.
In Tuesday's only second round match, Wimbledon runner-up Tomas Berdych overcame a stomach problem to see off Spain's Tommy Robredo 6-0 6-4.
The quarterfinal line-up is completed by fourth seed Tomas Berdych and Frenchman Richard Gasquet, who defeated Sam Querrey and Nicolas Almagro respectively.
On the men's ATP World Tour, sixth-ranked Tomas Berdych will play No. 8 Jo-Wilfried Tsonga in Sunday's final of the Marseille Open.
Djokovic will play Tomas Berdych who beat Fernando Verdasco 6-4 6-2 6-3.
France's Jo-Wilfried Tsonga will meet Tomas Berdych, from the Czech Republic, in the last eight after he beat Marcos Baghdatis 6-2 7-6.
Waiting in the final is Tomas Berdych, who beat a tetchy Juan Martin del Potro 7-6 (5), 7-6 (6) earlier in the day.
Fifth seed Tomas Berdych continued his strong start to the tournament with a comprehensive 6-2 6-2 6-4 defeat of Frenchman Guillaume Rufin .
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He was beaten 1-6 6-4 6-1 by unseeded German Philipp Petzschner, who will take on Czech eighth seed Tomas Berdych in the last eight.
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