The number 31 seeded Swiss knocked out the fourth seed with a 6-4 6-4 win in one hour and 40 minutes as she secured the first win over a top-five ranked player of her career.
“I served well and had some easy points on my serve because of that. It was a solid match,” said the 18-year-old Bencic.
“I’m happy. Very happy. I’m really excited. I always watched her on TV and when I was a small girl she was one of my idols, a role model for me and my game.
“So it makes me really proud to win today. It’s really a big moment for me.”
Elsewhere, second seed Maria Sharapova rolled to a 6-4 6-3 win over Victoria Azarenka to reach the fourth round at Indian Wells.
The 27-year-old Russian will now take on Italy’s Flavia Pennetta.
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