Australia trailed early but, just as they appeared set to steady and surge away, were reduced to 14 men for 20 minutes thanks to a Miles Amatosero red card.
Japan, coached by Eddie Jones and seeking their first win in eight encounters, smelt blood.
But the Wallabies, while unconvincing, did enough in 30 degree heat to win a second-straight Test and first under new coach Kiss to set up a tantalising rematch in Townsville next Saturday.
"The coaching team were very calm and collected, didn't let our emotions run," Kiss said.
"Made sure we managed our energy with 14 men, which was crucial.
"We had to find a way ... to repel them. Very proud of the effort in those conditions because we've seen what the Japanese team can do."
Japan led after a helter-skelter first 15 minutes, silky flyhalf Ryunosuke Ito slicing through staggered defence after Wallabies flanker Fraser McReight had won a penalty, tapped and run out of his defence only to turn the ball over with a speculative pass on halfway.
Harry Potter had an immediate reply though, the Wallabies going right then left before the winger ran back on the angle to score.
Flyhalf Declan Meredith continued to battle with his exit kicking, earning precious little ground to ensure Japan maintained the pressure.
But the visitors still slowly got traction, lock Josh Canham winning a penalty and Tom Wright the try-scorer after some rare fluency in attack.
They looked set to cross again from a driving maul in the right corner.
But the Japanese twisted it to a stop and Amatosero's rush of blood not only cost them the points but gave Japan a numerical advantage for 20 minutes they quickly exploited.
The lock, who has a reputation as a hot head after a preseason run-in with a NSW Waratahs teammate, had his left arm tucked when he attempted to clean out Japan captain Warner Dearns.
Dearns was moved by a tackler and Amatosero's shoulder appeared to hit the Hurricanes Super Rugby star in the head.
The yellow card was upgraded to a 20-minute red and it took Japan barely a minute to capitalise and lock it up at halftime.
Max Jorgensen barged over while the Wallabies were still down a man after the break, then the teams traded tries and Japan kicked a penalty to edge within six once Australia had 15 on the field again.
Fumbles kept Australia under the pump and Japan took another three to edge closer approaching the final quarter.
A penalty steadied them though and replacement prop Taniela Tupou easily burrowed over, under the posts, to stretch the lead to 10 with as many minutes to play.
Ben Donaldson entered the game at fullback, with Suaalii pushed to a wing when centre Isaac Henry became Wallaby No.999 with eight minutes remaining.
Japan weren't done though, winning a scrum penalty, peppering the line and Dearns finally crossing with two minutes to play.
The hosts had possession searching for the match-winner but spilt it in the final seconds to secure Australia an unconvincing win.
"We let ourselves down with some key fundamental errors and that was the difference," Jones said.
"But we're going to get better and next week's a great opportunity."
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