Seventh seed Nishikori won 6-4, 6-2, 6-4 in just over two hours on Hisense Arena and will face either world number one Novak Djokovic or French 14th seed Gilles Simon in the last eight.
"Today was one of the best matches I've had this week. Played good tennis, through in three sets," Nishikori beamed.
"I'm surprised that I broke him early every set. I was returning well today, so that made it tough for him to have a good serve all the time.
It is Nishikori's third Australian Open quarter-final and fifth overall in Grand Slams, one less than the Japanese record of six held by Jiro Satoh, who died in 1934.
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Nishikori's previous Slam encounters with the 2008 Australian finalist had both lasted five sets, but Tsonga was well beaten this time.
The lively Nishikori pounded the off-key Tsonga with five service breaks in their third Grand Slam meeting. The French ninth seed served eight double-faults and made 36 unforced errors in a flat performance.
He explained later: "I will say I was not really happy because I just want to challenge and didn't want it, because he said it's too late. Nothing to say about it. It's like this. Anyway, we have to play."
Nishikori's service was more effective than Tsonga, winning 74 percent of the first serve points and sweeping up 64 percent of the points on his second serve. He hit 31 winners, 16 off his strong forehand.
It also equalled Nishikori's best result at the Australian Open after reaching the last eight in 2012 and last year.
Nishikori became the first Asian man to play in a Grand Slam final when he was runner-up to Marin Cilic at the 2014 US Open, defeating Novak Djokovic and Stan Wawrinka along the way.
Nishikori trails Djokovic 2-5 in their overall head-to-head, and he has never faced Simon.