Notably, the match was delayed by rain on Monday, as Kohlschreiber was confident and displayed crisp gameplay on Tuesday morning. The unseeded German knocked off the five-time tournament champion 6-4, 6-4.
"I tried my best and I don't really have any regrets", said Osaka to media.
World No.1 Djokovic fell in straight sets in what was his first tournament since lifting a record seventh Australian Open title in January.
This win was her first victory over a No. 1 not named Williams. Osaka fired her coach and lost in the first round in Dubai before taking on a new coach, Jermaine Jenkins, who came on court during the match. I don't know. I'm still in the tournament feeling great, playing good tennis.
"It's a very special moment".
"To be honest, I don't enjoy losing, nobody does, but especially in a tournament like this, a tournament where I have had plenty of success in the past", Djokovic told reporters.
"It's a very special win today", Kohlschreiber said. "Completely different conditions today: Ball bounces much higher".
"He's been around for so many years and he doesn't really get overwhelmed by the occasion of playing on center court", he told reporters. "He deserved to win". For the 35-year-old veteran Kohlschreiber, this was his first victory over a No. 1 player in 12 tries, just his second win career-wise over Djokovic. "I must admit I was thinking about it, but it's part of our world, and we just have to bounce back very quickly".
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"I lose to Kholi and get absolutely shredded "same old Kyrgios", how about the guy is just good?"
Andreescu, who has won 23 and lost just three matches this year, will meet Spain's Garbiñe Muguruza next following the former world number one's 5-7, 6-1, 6-4 win over Kiki Bertens. Kohlschreiber converted three of his four chances.
Here are five things to know about Kohlschreiber ahead of his fourth-round match against Gael Monfils on Wednesday in Indian Wells.
Djokovic remains alive in doubles with partner Fabio Fognini.
The loss ended Djokovic's seven-match winning streak over Kohlschreiber.
"I think I felt good from the beginning", said Federer.
Nadal, a three-time victor of the Indian Wells title, next faces Serbian qualifier Filip Krajinovic, who ousted 14th-seeded Russian Daniil Medvedev 6-3, 6-2.
The big-serving 2012 Indian Wells finalist will face Russian Karen Khachanov after he defeated countryman Andrey Rublev 7-5 6-3 in their fourth round match.