Federer pounced in the opening game to break serve, then broke the unseeded Frenchman again at 4-2 to mow through the first set.
The Swiss second seed broke again early in the second and charged through the third, sealing the match in 83 minutes with an imperious forehand passing shot.
Despite the ease of the win, Federer was typically complimentary of his opponent in his post-match appraisal - and defended his decision to not play any warm-up tournaments.
"Benoit's a good player, a good talent," he said. I haven't played a match this season yet. You're not sure [how you're going to play] and that's why you're relieved when you get through the first one.
"I've had a few busy years since I had kids. I just wanted to cool down a bit. It's nice to enjoy the off season.
"I hope it's the right decision, we'll see how it goes. I'm confident in my play."
Federer won the pair's only previous encounter in straight sets. He will next play Dudi Sela of Israel as he continues his quest for an 18th Grand Slam title.
Sixth seed Juan Martin del Potro eased through 6-1 6-2 6-2 against Adrian Mannarino.
The Argentine needed just 76 minutes to sweep aside the world number 170, sealing the first set in just 22 of those minutes without committing a single unforced error - and it did not get much better for Mannarino from there.
He needed four sets to beat the Frenchman at the same stage last year.
Del Potro, the only player outside the 'big four' of men's tennis to have won a Grand Slam in the last eight years - the US Open in 2009 - remained circumspect about his chances of breaking back into the elite.
"I played really well," he said. "I remember last year when we played the first round also, and he had a better match than today.
"But I think I played really aggressive. I made a lot of winners with my forehand. I served well. I made very good start to this Open."
Despite the absence of the injured world number four Rafael Nadal, Del Potro was not confident of emerging from a half of the draw which also includes Federer and the newest member of the Grand Slam winner's club, Andy Murray - who also won on Tuesday.
"They are so far from me at the moment," he added. "We play five sets and matches can be tough for all the players, so I (am) just thinking about my second round. Hopefully I can go far, but I need to play better and better.
"I think the favourites are the same even if Rafa is not here. If Rafa was here, he would be a favourite for sure also. But Roger, Novak, Andy Murray, and other guys are the favourites to win the tournament."
Del Potro will face Germany's Benjamin Becker in the second round on Thursday.
Still only 24, he reached the quarter-finals at three of the four Slams last year, including at Melbourne Park, but he knows from experience what it takes to go those extra three steps.
"I'm here trying to do that, but it's not easy," he said. "I know how tough it is to win a Grand Slam. But I also know the way to win a Grand Slam.
"So I'm trying to do that for this year. Could be my biggest challenge this year, to win another Grand Slam. But they are playing really good tennis, and it's not easy."
Flamboyant Frenchman and seventh seed Jo-Wilfried Tsonga had little trouble in overcoming compatriot Michael Llodra 6-4 7-5 6-2 to book his place in the second round.
He now meets Go Soeda after the Japanese player disappointed home fans with a 6-7(4) 6-3 6-2 6-3 win over wild card and reigning Australian Open Junior champion Luke Saville of Australia.
France's ninth seed Richard Gasquet won through 7-5 6-2 6-1 against Albert Montanes of Spain.
Gasquet was 5-3 down in the first set but won four straight games to take it - and his opponent never recovered from that blow.
Gasquet will play Alejandro Falla in round two.
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