"It was very tough from the start -- Berdych has had a great year, " he added.
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.
"I'm going to do everything the same like I do before every game, " Berdych said.
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.
"It's going to be very tough, Berdych is having his best year on the tour, " added Djokovic.
Third seed Tomas Berdych moved into the third round, with the Czech defeating Spain's Pere Riba 7-5 6-1.
"It was a great match, definitely, " said Berdych, who had beaten Federer in the early hours of Wednesday.
The Swede will now meet Tomas Berdych after the Czech giant-killer battled back to see off Fernando Verdasco.
The Swiss no.2 must win the first singles match against Berdych on Sunday to keep the tie alive.
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.
But Berdych had some bad luck when a net cord bounced out and Djokovic closed out the set.
BBC: Novak Djokovic makes short work of Berdych in Melbourne
Put Nadal on a wet clay court with Djokovic or even Gulbis, Roger Federer, or Tomas Berdych and he could suffer.
Czech Berdych was appearing in his first final of the 2013 season, but was left to rue missed opportunities.
But Berdych gave a performance of the very highest order to set up a semi-final meeting with Novak Djokovic.
The Serb raced into a 5-2 lead, only for Berdych to neutralise the break with a dipping forehand winner.
BBC: Novak Djokovic makes short work of Berdych in Melbourne
He fought from behind in the quarter finals against Marin Cilic and the semis against Tomas Berdych.
FORBES: Andy Murray's Management Change Pays Off at the U.S. Open
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.
But Berdych's fighting spirit saw him take the final two sets 6-4 6-4 to leave the teams tied at 1-1.
The Swiss top seed was beaten 6-4 3-6 6-1 6-4 to give 24-year-old Berdych the biggest victory of his career.
Berdych triumphed 6-3 6-4 3-6 7-6 (7-5) in more than three hours against Wawrinka, who had beaten Rosol on Friday.
Berdych will now look forward to next week's 100th Davis Cup final, where he will lead his country against Spain.
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