The former world number one, coming off a wretched 2013, channelled the halcyon days of his new coach Stefan Edberg, swooping at the net to fell the stunned Frenchman at an electric Rod Laver Arena.
Having suffered early exits at Wimbledon and the U.S. Open, Federer muscled into his 41st grand slam quarter-final, equalling the record of American Jimmy Connors in the professional era.
Under the watchful eye of Edberg - one of the game's finest serve-volleyers - the Swiss master fittingly sealed the match with an imperious cross-court volley and declared the crisis of confidence that blighted last season banished.
"For me personally, I've overcome it, I don't have doubts anymore," the 32-year-old told reporters.
"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 was a big test for me.
"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."
Having mauled a string of unheralded opponents in his three previous matches, Federer braced for his biggest test against the flashy Frenchman, who dumped him from the Roland Garros quarter-finals in straight sets.
Federer picked apart his opponent's serve twice in an opening set boasting 14 points won from 17 rushes to the net, and sealed it when Tsonga pushed a lob into the tramlines.
The Frenchman battled to keep the match on serve in the second set but it all came unstuck at 5-5.
He saved a break point with an ace, but Federer raised a second with a sliced backhand that the net cord dropped unkindly onto the Frenchman's side.
Sealing the set with an ace, Federer then ensured there would be no repeat of the marathon five-setter he needed to knock out Tsonga at last year's quarter-finals.
Trailing 4-2 in the third set with three break-points against him, an exasperated Tsonga howled in frustration, earning a warning for bashing a ball into the night sky.
He saved them all to close out the game and slammed his racket into his chair in a bid to pump himself up.
But in the following game, the Frenchman dumped his sole break point chance into the net allowing Federer to march on, and serve out the final game to love.
Wednesday's clash against fourth seed Murray will be a re-match of last year's semi-final in which the Briton won a thriller in five sets.
With eight-times grand slam champion Ivan Lendl in Murray's corner, both players will rack the brains of their 1980s legends turned super-coaches in a bid to find an edge.
"He did things his way back in the day," Federer said of six-times grand slam champion Edberg.
"I'm sure things were different back then. But still you can take so many things from his experience. I want to say maybe try out a few things that worked for him, try out a few things that he thinks would work out for me this time around.
"I feel like I can think ahead. I can think tactics. I can think many things out there ... I've overcome a lot in the last few months."
(Reporting by Ian Ransom; Editing by Justin Palmer)
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