It was a vintage performance from Federer, who chalked up 43 winners in 6-3 7-5 6-4 victory.
Age appeared finally to be catching up with the great man last season as he endured his worst year in more than a decade, dropping as low as seventh in the rankings and seeing his run of consecutive grand slam quarter-finals ended at 36.
But Federer always insisted his struggles were largely caused by back problems, which he overcame towards the end of the season.
He began this year with a full winter's training behind him and a new, larger-headed racquet, and if he can maintain the same form he showed against Tsonga for the rest of the tournament, then an 18th grand slam title is not out of the question.
Federer said: "I don't have doubts any more. I know I'm going definitely in the right direction. I've had a great off season. I had a strong end to the year. I couldn't have worked harder in the off season.
"This is the type of win I needed. Clearly if I lose in the next round I'll have doubts again, but I'm going to try to not make that happen.
"What I've shown over the last three to four months to myself is that I'm more confident, that I know I'm most likely going to play okay in my next match, which wasn't always the case midway through last year when I didn't know how I was going to feel during the match.
"I feel like I can think ahead. I can think tactics. I can think many things out there. Everything else but my body, and that's very positive. I've overcome a lot in the last few months."
More doubts surround Murray, who is playing in only his second tournament since back surgery last September.
Wednesday's clash will be a rematch of their semi-final meeting from last year, which Murray won in five sets before losing to Novak Djokovic in the final.
Federer said: "I don't know how he's feeling. I haven't seen him play much.
"But what I'm hearing is that he's fine. That's very positive. That's what I was hoping for Andy, that when he did come back, he was 100 per cent, not half way, limping, not feeling great.
"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 we played was a great match. So I hope we both can reproduce something similar.
"It will be interesting, because we had an interesting year last year with some ups and downs. It's a good start to the season for both of us already."
Federer made the perfect start on Monday with a break of the Tsonga serve and the pressure was all coming from the Swiss.
Tsonga, who beat Federer in straight sets at the French Open last year, held on until 5-5 in the second set but then dropped his serve twice in three games.
His only break point came after he fought back from 0-40 at 2-4 in the third but he could not take it and that was that.
Federer was particularly successful coming to the net, something that is bound to have pleased his new coach Stefan Edberg, who celebrated his 48th birthday on Sunday.
The Swiss said: "I'm extremely happy how things went for me tonight. I was able to play my game, offensive, mix it up, come to the net. I was surprised that things worked out for me.
"This was the kind of match I was hoping to play maybe against Jo in Paris in the quarters. I got a hiding that time.
"This is nice being back in the quarters, because I haven't been in one for two (grand slams) now, Wimbledon and the US Open. So I'm back on a streak of 36, we'll see where it goes."