Federer defeated 23rd seed Kyle Edmund by 6-1, 6-4.
They are a round away from meeting for the 39th time in their illustrious careers, and for a fourth time at Indian Wells.
Krajinovic will be a big underdog when he faces Spain's world number two Rafa Nadal, who crushed Argentine Diego Schwartzman 6-3 6-1 on the showcase court to reach the last 16.
"I'm really happy about it, especially since I didn't really do anything before this", said Kecmanovic, who will take on Canada's 13th-seeded Milos Raonic in the quarters.
Nadal, meanwhile, himself a 17-time Grand Slam champion and the current world number four, beat Serbia's Filip Krajinovic 6-3, 6-4 in one hour and 26 minutes.
The 24-year-old, now ranked 23 in the world, won 84% of his first-serve points to triumph 6-3 6-3 in an hour and 14 minutes. "It's one of these victories today I'm really proud of", Nadal told reporters, declining to absolutely guarantee that he would be okay to play on Saturday. I was able to mix up my game, cover my serve, be risky on the return.
"The previous days here in Indian Wells helped me a lot to get back to my top level physically and also to play good tennis again", Thiem said. 2 has finally reached the quarter finals of ATP Indian Wells for the first time in three years.
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"Maybe because of the conditions".
"It will be amusing that somebody other than Novak is still in", Kecmanovic said of top-ranked Djokovic, his famous countryman who was upset on Tuesday.
The Spaniard will play Karen Khachanov next following the Russian's 6-4 7-6 (7-1) win over John Isner.
Kecmanovic got into the main draw when world No.6 Kevin Anderson withdrew before his opening match with an elbow injury.
The 13th seed will square off against France's Gael Monfils, a 6-0 6-2 victor over Germany's Philipp Kohlschreiber, in the quarter-finals on Thursday.
Raonic sent down 12 aces in his 6-4 6-3 win over German Jan-Lennard Struff to set up a clash with lucky loser Miomir Kecmanovic, the Serbian teenager progressing when Yoshihito Nishioka retired after losing the first set 6-4.