The 20-time Grand Slam champion came through 6-3 6-4 for his sixth straight win over Wawrinka, setting up a match with Britain’s Kyle Edmund.
"I think I felt good from the beginning," said Federer. "I think for me the plan worked. I was able to mix up my game, cover my serve, be dangerous on the return. Maybe take some rhythm away from Stan, like I always try to do, but you can't always make it work."
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British number one Edmund booked his spot in the fourth round at the BNP Paribas Open with a straight-sets win against qualifier Radu Albot in Indian Wells.
The 24-year-old, currently 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 put an end to Albot’s nine-match winning streak, after the 29-year-old Moldovan claimed the maiden tour title of his career at Delray Beach last month.
Federer said of his next opponent: "I have never played him, and so that's exciting, especially an established player… I think he's a really nice guy. Trains hard. He's got good balance. Very similar backhand to [Andy] Murray in some ways, also, by the technique of it. And the forehand really goes."
With additional reporting from PA Sport
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