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Stunned by the young Canadian's power serving in the opening set, the Swiss maestro delivered a master class in the next two, sealing victory in just over two hours when the towering Raonic netted a forehand.
Federer, who had never previously played the 21-year-old Canadian, will next face Brazilian Thomaz Bellucci, who benefited from a walkover when Russian Nikolay Davydenko withdrew due to illness.
"For me it was a difficult match," Federer said in a courtside interview after receiving rapturous applause from the near-capacity crowd at the Indian Wells Tennis Garden. "I've never played him before.
"He's probably seen me play a whole lot of times on TV which helps him out a bit. But I really did well. I hung in there and played a great second set.
"The third set was close and I'm happy to be moving on in the tournament," added the Swiss, who had swept past American Denis Kudla 6-4 6-1 in the previous round while shaking off a flu bug and slight temperature.
On a cool evening in the California desert, the opening set went with serve and into a tiebreak that Raonic won 7-4 when Federer hit a forehand service return long.
However the Swiss immediately broke the Canadian in the next game, firing a pinpoint forehand winner down the line to lead 1-0. He again broke in the fifth when he blasted a forehand past Raonic who was stranded at the net to go 4-1 up.
With the crowd eagerly watching the action on the showpiece stadium court, world number three Federer comfortably served out to level the match at one-set all.
The final set went with serve until the seventh game when Federer coolly set up a break point with a whipped forehand winner and immediately took advantage when he passed Raonic with a crunching backhand winner down the line to lead 3-4.
Federer, who clinched three consecutive titles at Indian Wells from 2004, served out to seal the win, wrapping up victory on his first match point after a crunching forehand winner down the line had put him 40-15 up.
Federer paid tribute to emerging talent Raonic, who has already has recorded five victories over top-10 players.
"He serves really well and he's going to be for sure a future top-10 player, and a whole lot better," the 16-times grand slam champion said. "He did very well on Tuesday night under pressure as well."
