Djokovic handled 18th-seeded John Isner in straight sets, 6-4, 7-6 (7-5) in the final match of the night. He will face 32nd-seeded Bernard Tomic, who beat Thanasi Kokkinakis, 6-4, 4-6, 6-4.
Djokovic, the reigning Australian Open and Wimbledon champ, won this event for a third time last year when he topped Federer in a marquee finale. The Serb was runner-up in 2007 to Rafael Nadal.
The second-seeded Federer needed just 69 minutes to knock off Jack Sock 6-3, 6-2 in their fourth-round match.
Three-time champion Nadal, seeded No. 3, also moved on with a 6-2, 6-4 win over 13th-seeded Gilles Simon in 78 minutes.
Federer moved on to face No. 9 seed Tomas Berdych, who won an all-Czech match against 27th-seeded Lukas Rosol 6-2, 4-6, 6-4. Nadal will play Canadian Milos Raonic, seeded sixth, who beat 17th-seeded Tommy Robredo 6-3, 6-2.
Former runner-up Andy Murray, seeded No. 4, cruised past left-hander Adrian Mannarino 6-3, 6-3 on the hardcourts at the Indian Wells Tennis Garden.
Murray, who lost to Nadal in the 2009 final, will meet another southpaw, No. 12 seed Feliciano Lopez, in the quarterfinals. Lopez beat fifth-seeded U.S. Open runner-up Kei Nishikori 6-4, 7-6 (7-2) on Day 7 in the California desert.
The winner of the first ATP Masters event of the season will claim $900,400.