The 19-year-old Russian Red Bull protege beat four-time champion Sebastian Vettel, 2009 champion Jenson Button, and 2007 title winner Kimi Raikkonen on his first visit to the Albert Park street circuit.
He will line up eighth on the grid for his grand prix debut, while team-mate Jean-Eric Vergne will start sixth as STR bounced back from a troubled time in free practice to star in the wet qualifying sessions.
"It's a good feeling," said Kvyat when asked by AUTOSPORT for his thoughts on beating such illustrious names.
"It was a good qualifying. I was pushing very hard but didn't feel any big pressure.
"It was quite extreme for me. I had to find all the references immediately. Here is a particularly tricky track because of the white lines everywhere. It was making the car very tricky.
"On the traction we still have some work to do, but it was very good to show and to know that we can be in the top 10. P8 is a very good place to start from.
"Three or four weeks ago, if you'd said we'd be P8 and P6 we'd be very very happy. It's a small surprise for us but a very positive one. But we knew we could be competitive in the wet."
Kvyat struck the barriers at the end of the final session after aquaplaning off between Turns 11 and 12, but does not think the moment cost him too much.
"I took the white lines and had a massive oversteer on a straight line. Not really my mistake. It happens," he added. "We were coming faster but I don't know where it would have put me."
VERGNE RUES LOST FOURTH PLACE
Team-mate Vergne said he was not surprised by Toro Rosso's pace, after making the top six in qualifying for the first time in his F1 career.
"I knew that when we got everything together that we had a good car. I've said all winter that I feel a good car," said the Frenchman.
"We have a decent car, maybe not for the podium, maybe not for Q3 every weekend, but at least we are able to do some good stuff with it as we showed today.
"When I look back at my lap in Q3 it was a bit of a shame because there were massive puddles and for the first time they showed yellow flags for debris at Turns 11 and 12 and I had to release four tenths.
"With these four tenths I would have been P4. I'm so mad at it. P4 was possible, but I'm still happy with sixth."
- Sports & Recreation
- Motor Racing
- Jenson Button
- Sebastian Vettel
- Kimi Raikkonen
- Jean-Eric Vergne