Osaka surprised the tennis world when she parted with coach Sascha Bajin shortly after winning the Australian Open and moving to number one in the world.
"I think it gives me confidence that I can turn around matches, that I can play also three sets, also in the close moments that I'm there, that I can trust myself", said Kerber, adding that it was always hard to face an opponent for the first time. But I feel pretty good right now, because I tried my best and I don't really have any regrets.
"I think I did well", she said.
Bencic, who turned 22 on Sunday, was a teenage star who won two titles in 2015 but saw her career stalled by a string of back and wrist injuries.
She will have another shot at a top-10 player when she takes on hard-hitting world number five Karolina Pliskova, who smashed 13 aces to dispatch Anett Kontaveit 7-6 (0) 4-6 6-2 to reach the quarter-finals.
The victory over Osaka came in "very high" in her list of big wins.
It was a tough day for seeded players at the BNP Paribas Open, with Novak Djokovic and Naomi Osaka, the world's top-ranked players, ushered out in the desert. I think I played a little bit wrong. "It's not going to get any easier from here, so I just have to continue to raise my game". He kept fighting and putting ball in the court and I made a few mistakes. "So just things worked out for me", said Bencic.
Venus Williams beat Christina Mc Hale to reach the Indian Wells fourth round. AP
Despite the loss, Osaka is guaranteed to lead the rankings after the tournament since world number two Simona Halep also lost on Tuesday.
Halep, who received medical treatment for blisters on her foot during the match, won less than half of her first-service points and hit just six winners to go with 36 unforced errors. I was running too much and too defensive. I knew that she's young, and she has nothing to lose today.
Osaka said the first title defense of her career had brought different challenges, and she thought she handled them well.
Naomi Osaka (JPN) waves to fans while leaving the court after being her fourth round match against Belinda Bencic (not pictured) in the BNP Paribas Open at the Indian Wells Tennis Garden. No. 8 Angelique Kerber outlasted qualifier Natalia Vikhlyantseva 3-6, 6-1, 6-3 and No. 9 Aryna Sabalenka defeated 24th-seeded Lesia Tsurenko 6-2, 7-5.
Canada's Bianca Andreescu, 18, continued her remarkable season with a 7-5 6-2 win over China's Wang Qiang. "Yeah, I think I did well for my first time".
The U.S. and Australian Open champion, who is also defending the title at Indian Wells, will next face Switzerland's Belinda Bencic, who beat Ekaterina Alexandrova 6-4 6-2.