Kyrgios, seeded 17, needed three tiebreakers to win a crunch match with the former finalist 7-6 (7/5), 4-6, 7-6 (8/6), 7-6 (7/5) in 3hr 17min in a spectacular night match on Rod Laver Arena.
It pitches the mercurial Australian into a round of 16 showdown with Bulgaria's world No.3 Grigor Dimitrov on Sunday.
Kyrgios, urged on by his home crowd, traded breathtaking shots with Tsonga, who lost to Novak Djokovic in the 2008 Australian final when Kyrgios was a doting 12-year-old fan.
"He was a guy I looked up to as a kid, still do, he's a great guy. I'm just so happy to get through.
"At 5-2 down in the fourth set breaker, I was getting ready for a fifth set mentally. I somehow just hung in and got a couple looks (at the serve).
"I knew my best chance was probably to get in a couple tiebreakers.
"He served extremely well throughout the whole match. I didn't really get a look at many second serves at all."
"He has got it. Yeah, we will see how it goes for him. But anyway, he's already a good player," Tsonga said.
"I think he still needs time to improve. With his game already, he can do some damage. The most important in tennis I think is to believe in it."
The match had some drama just after the third set when an incensed Tsonga yelled at the chair umpire in French about a vociferous member of the crowd.
Tsonga was heard to say "bring him here, he needs to come down here".
Tsonga was then issued with a code violation for unsportsmanlike conduct.
Tsonga explained later: "The guy was telling me, 'You are under pressure now, you are under pressure now,' when I was bouncing my ball. That's it. I lost it and I went a little bit crazy."
Kyrgios won his first home ATP Tour title at the lead-up Brisbane International -- beating Dimitrov along the way -- and is looking to go further than a quarter-final appearance in Melbourne three years ago.
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