In a tournament full of surprises, Federer and Djokovic struck a blow for the old world order with Federer beating Germany's Tommy Haas 6-4 6-4 and Djokovic coming back to down Croatia's Marin Cilic 1-6 6-2 6-3.
Federer and Djokivic are the only players ranked in the world's top 10 to reach the quarter-finals after Wawrinka and Murray joined the big-name casualties when they both crashed to lower-ranked opponents on another day of upsets in the Californian desert.
Wawrinka suffered his first loss this year when his 13-match winning streak came to a shuddering halt as he was beaten 7-6(1) 4-6 6-1 by South African Kevin Anderson.
"It wasn't really on my mind that he had won Australia," said Anderson, whose next opponent is Federer.
"It feels great to beat somebody who obviously has just won a grand slam."
Murray was blown away by Canada's Milos Raonic, one of the biggest servers in men's tennis.
Despite winning the first set, the Scotsman was unable to contain the raw power of Raonic, who triumphed 4-6 7-5 6-3 in a little over two hours.
Raonic blasted 15 aces past his bewildered opponent, who is one of the best returners in the game, and won a staggering 83 percent of points when he landed his first serve.
Murray did break Raonic's serve in the opening set and again in the deciding third to lead 2-1 but lost the next four games in a row against the 6ft 5in (1.96 metre) tall Canadian.
"To get broken two consecutive times in that situation isn't good enough. I played poor tennis at that stage. I didn't make enough balls and I missed some really easy shots," Murray told reporters.
"It's tough to win matches like that, because against him, he obviously wins a lot of free points with his serve. So over the course of the set, if you give up enough unforced errors on basic shots, then with the amount of free points he gets on his serve, that's going to add up to a negative result."
Raonic's next opponent in the quarter-finals will be Ukrainian giant killer Alexandr Dolgopolov, who followed up his upset victory over Rafa Nadal on Monday with a comprehensive 6-2 6-4 drubbing of Italy's Fabio Fognini.
"I think the most important thing is obviously my serve and the beauty of that is nobody can affect me," Raonic said.
Already a four-time champion at Indian Wells, Federer is now on a nine-match winning streak after taking the title in Dubai before heading to Indian Wells but said he was wary about Anderson, who has reached a career-high ranking of 18 after making the final of his last two tournaments.
"I know how tough he is," Federer said. "He's the best here usually in the States, outdoors on the hard courts. That's when he's had his biggest success.
"I'm aware that this is not going to be an easy match just because he's not ranked in the Top 10."
Djokovic had won each of his previous seven encounters with Cilic but his perfect record was in danger after he lost the opening set to the towering Croatian, winning just three points on return.
But the Serbian quickly got his act together, and broke Cilic twice in the second set then once in the deciding third to safely advance to the last eight.
John Isner kept American hopes alive with a 7-6(3) 3-6 6-3 win over Spain's Fernando Verdasco, while Latvia's Ernests Gulbis defeated Roberto Bautista of Spain 7-6(0) 4-6 6-2.
A third Spaniard, Feliciano Lopez, was sent packing by unseeded Frenchman Julien Benneteau, losing 6-3 7-6(4).
BNP Paribas Open results
2-Novak Djokovic (Serbia) beat 24-Marin Cilic (Croatia) 1-6 6-2 6-3
17-Kevin Anderson (South Africa) beat 3-Stanislas Wawrinka (Switzerland) 7-6(1) 4-6 6-1
10-Milos Raonic (Canada) beat 5-Andy Murray (Britain) 4-6 7-5 6-3
7-Roger Federer (Switzerland) beat 11-Tommy Haas (Germany) 6-4 6-4
12-John Isner (U.S.) beat 30-Fernando Verdasco (Spain) 7-6(3) 3-6 6-3
20-Ernests Gulbis (Latvia) beat Roberto Bautista (Spain) 7-6(0) 4-6 6-2
28-Alexandr Dolgopolov (Ukraine) beat 13-Fabio Fognini (Italy) 6-2 6-4
Julien Benneteau (France) beat Feliciano Lopez (Spain) 6-3 7-6(4)
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- Marin Cilic
- Milos Raonic