Djokovic held off a strong fightback by Spaniard Pablo Andujar to triumph 6-0, 6-7, 6-2, Federer recovered from a shaky first set to beat Brazilian Thomaz Bellucci 3-6 6-3 6-4 while Nadal eased through 6-3, 6-2.
Argentina's David Nalbandian upset sixth seed Jo-Wilfried Tsonga of France 3-6, 7-5, 6-3 and seventh seed Tomas Berdych was beaten 6-4, 6-0 by Spaniard Nicolas Almagro, who had lost a bad tempered fourth-round match to the Czech at the Australian Open in January.
Almagro's reward for reaching the last eight at Indian Wells for the first time is a matchup with Djokovic.
World number one Djokovic battled past unseeded Spaniard Andujar at the Indian Wells Tennis Garden after barely breaking sweat with an attacking display in his opening set.
However, the Serb fell 7-5 in a second set tiebreak as Andujar upped his game on the showpiece stadium court.
Champion here in 2008 and last year, Djokovic broke his opponent in the first game of the third set, and also in the seventh, before sealing victory on his first match point when the Spaniard hit a forehand service return wide.
"My opponent is really a quality player who deserves to be at this stage of the tournament," Djokovic said in a courtside interview. "He surprised me with his aggressive approach. He was taking the ball early and was playing well.
"In the second set, I start playing a little bit more defensive and I think that allowed him to come back to the match. All the credit for him to play the way he played.
"And then in the third set I regrouped. I managed to stay calm mentally and just find my rhythm again," added the Serb, who won his fifth grand slam crown at the Australian Open two months ago.
Nadal, Indian Wells champion in 2007 and 2009, broke pony-tailed Ukrainian Dolgopolov once in the opening set and twice in the second to wrap up a commanding win in one hour, 16 minutes.
"He is a very difficult player to play against," the Spanish left-hander said of Dolgopolov. "He hits very hard, produces winners from every part of the court. He is a funny player, good for tennis.
"I started very strong and he made a few mistakes, more than usual, with his backhand, which helped me a lot. Being in the quarter-finals here is fantastic for me," added Nadal, who has reached the semi-finals in his last six attempts at Indian Wells and will next take on Nalbandian.
For the second day in a row, triple champion Federer lost the opening set but he then broke Bellucci in the first and ninth games of the second to level the match.
The final set went with serve until the Swiss maestro broke the 50th-ranked Brazilian in the 10th game, converting his second match point when the left-hander hit a forehand long.
"It's always great to come through in a three-setter," said 16-times grand slam champion Federer, who has been trying to shake off a flu bug and slight temperature. "I thought Thomaz played great.
"I struggled early on to make the transition from night (session) to day. I'm happy and relieved to be through and still alive in the tournament."
Federer will next play ninth seed Juan Martin del Potro of Argentina who overcame Uzbekistan's Denis Istomin 7-6 6-7, 6-2.
Big-serving American John Isner powered past Australian qualifier Matthew Ebden 6-4, 7-5 to set up a meeting in the last eight with Frenchman Gilles Simon, who beat American Ryan Harrison 7-6, 5-7, 6-1.
