Federer broke 10th-seeded Tsonga in the second game of the match and was one set up in under 30 minutes.
In an almost flawless performance, the Swiss maestro barely dropped a point on his serve in the first set.
He continued that dominance - Tsonga didn't get a break point on the 17-time major winner under he was trailing 3-4 in the third - and he didn't convert.
The 32-year-old was "extremely happy'' with his performance and said it was almost better than he had hoped for.
"I'm very pleased - I don't think I got broken today and that was against a great player.
"I was able to play my game, offensive, mix it up, come to the net.
"Yeah, I was surprised that things worked out for me,'' Federer said.
He said it was the match he had wanted to play against Tsonga in the quarter-finals of the French Open last year, which the Frenchman won in straight sets.
That was the last quarter-final that Federer made, missing the final eight at Wimbledon and the US Open.
It also equals US great Jimmy Connors' record of 41 grand slam quarter-finals.
"It's nice being back in the quarters, because I haven't been in one, you know, for two now, Wimbledon and the US Open.''
Under the guidance of new coach, Swedish great Stefan Edberg, Federer was more aggressive at the net and reaped the rewards, winning 34 from 41 points.
Tsonga was unable to find any rhythm in his game.
Last year Federer met Murray in the semi-finals at Melbourne Park and lost in five.
"It's good to see he took care of his draw, and here we are again.
"I'm looking forward to the match, I must say.
"I wonder how it's going to play out. Last time was a great match so I hope we both can reproduce something similar.''
Tsonga said Federer had played ``unbelievable'' tennis.
"I was not surprised because, you know, when you play Roger, you expect him at this level,'' Tsonga said.
"You know he's able to play like this, so you always expect it.''
He said he just couldn't find a way to stop Federer's momentum.
"I was not enough good, you know, to give him a good opposition, and that's it.
Today's schedule
Day Session
Li Na (4), China, vs. Flavia Pennetta (28), Italy
Ana Ivanovic (14), Serbia, vs. Eugenie Bouchard (30), Canada
Tomas Berdych (7), Czech Republic, vs. David Ferrer (3), Spain
Night Session
Stanislas Wawrinka (8), Switzerland, vs. Novak Djokovic (2), Serbia
Alex Bolt and Andrew Whittington, Australia, vs. Daniel Nestor, Canada, and Nenad Zimonjic (8), Serbia
Show court 3
Junior Boys' Doubles - Round 2
Oliver Anderson (AUS) / Alexander Klintcharov (NZL) vs. Andrey Rublev (RUS) [2] / Alexander Zverev (GER) [2]
Court 20
Junior girls - Round 2
Tereza Mihalikova (SVK) vs. Rosie Cheng (NZL)
- AAP
