Federer defused the 22-year-old Canadian's serve and held his own comfortably before shifting up the gears when necessary to race to a 6-4 7-6 6-2 victory in a little under two hours.
After world number one Novak Djokovic was taken to the brink of defeat in a five-hour thriller against Federer's fellow Swiss Stan Wawrinka on Sunday, there was much anticipation that the second seed could face a similar challenge.
Big-serving Raonic had taken a set off Federer in all three of their previous meetings but even that never looked likely in their fourth-round clash on a cool Rod Laver Arena.
Federer wrapped up the first set when Raonic netted a volley, the second with a brilliant forehand down the line to take the tiebreak 7-4, and the third with another big forehand winner.
"I felt good out there," the 31-year-old said. "I was moving well, had good anticipation and reaction today, which was key obviously on the return. In the third set I started to feel extremely good on the return.
"I played well. I think I played tactically well tonight and was able to keep the points short on my own service games."
The 17-times Grand Slam champion, who is chasing a fifth title at Melbourne Park, will meet seventh-seeded Frenchman Jo-Wilfried Tsonga in the last eight after the Frenchman ramped up his serve and blasted compatriot Richard Gasquet off the court 6-4 3-6 6-3 6-2.
The only man in the tournament who has yet to lose a service game, Federer gave up only five points on his first serve in the match against Raonic.
"Tonight was a very solid night, so I'm very happy," he said. "If I can maintain such a level of play, obviously I'm happy I give myself a chance of going deep in this tournament, which is obviously the goal."
Despite the lesson he handed out to Australian Bernard Tomic in the third round and Raonic on Monday, Federer said he no longer felt he had to make a statement when was playing talented youngsters.
"Maybe five years ago, today I'm in a different place. I just try to go out there and play my best, regardless if they're young or not," he said.
"But I get a lift in terms of energy playing against those kind of guys. But I don't try to hit harder or intimidate them because they've seen the big serves and they've seen the great movement around. They know what it's all about.
"I don't play so much with the fear factor and all that stuff. I really just try to beat them. That's the only thing."
Federer has accumulated so many records in his glittering career that extending his mark for most successive last eight appearances at a Grand Slam was never going to excite him too much.
"Obviously times have changed," he said. "Conditions have slowed down. That gives you an opportunity to maybe be more consistent in all four majors.
"I'm happy to have another one ... But does it drive me? I don't know, I'm not sure. It's a nice record to have. Obviously as it's ongoing, you try to keep working at it."
In his match, Tsonga won more than 80 percent of points on his first serve and clubbed 37 winners to bring an end to Gasquet's challenge after the ninth seed had battled back to win the second set.
The 27-year-old wrapped up victory with another huge serve after 140 minutes to level up their career head-to-head at 4-4 and join another Frenchman, Jeremy Chardy, in the last eight.
Tsonga, who beat Gasquet at the same stage of the 2008 tournament on the way to his only Grand Slam final, now has his work cut out if he is to advance at the expense of the incomparable Federer.
His record against Federer is poor - 8-3 in the Swiss's favour - but Tsonga knows how to beat Federer in a Grand Slam, having done so at Wimbledon in 2010.
Tsonga appointed Australian Roger Rasheed as his coach late last year and said the man who helped both Lleyton Hewitt and Gael Monfils could be his secret weapon.
"It's great because he's always positive," Tsonga told reporters. "He wants to win maybe (even) more than me. He's incredible.
"I try to be at his level and have exactly the same motivation because I think he can move some mountains because he's very motivated."
Rasheed may not be able to speak French - Tsonga said the best he can manage is "bonjour" - but his words appear to be having a good effect on the Frenchman's state of mind.
"I was surprised because every day when I come to practice, he's giving me a lot of energy just by his talk, and it's great," he said.
"Then on the court I just try to put what I do in practice on the court because on the court I am alone.
"But I'm practising well. When you work hard and you're focused on what you're doing, you are obliged to improve again. Even if it takes time, for sure I will improve my game."
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