The Wallabies were forced to dig deep, battling the heat as well as being a man down, holding off a strong comeback from Japan to emerge victorious.
"That was tough, wasn't it? Not just the conditions," said Kiss. "They're a good team. They play fast and hard at home in their backyard.
"Probably offered a few too many opportunities for them. We'll have a look at it. But overall, that's a Test win. Well done, boys."
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Kiss took over from Joe Schmidt as head coach last month after Australia finished the first phase of the Nations Championship with one win in three - a victory over Italy following on from losses to Ireland and France .
For Australia's two-Test series against Japan, Kiss included only one uncapped player, centre Isaac Henry, but recalled big, versatile Reds forward Lukhan Salakaia-Loto and left out veteran James Slipper.
The Wallabies were forced to scramble after Amatosero was red-carded in the 32nd minute for a dangerous clean-out on Warner Dearns. Initially shown a yellow card, it was upgraded to red just before the break, which the teams entered locked at 14-14.
Tries from Max Jorgensen and Fraser McReight early in the second half helped Australia build a nine-point lead but Japan steadily ate into that advantage with a pair of penalties from Takuro Matsunaga.
The quality of Australia's bench proved the difference as it allowed the visitors to keep up the pressure on Japan, and Taniela Tupou crashed over to give them a 10-point lead with 10 minutes remaining.
Japan captain Dearns set up a grandstand finish when he found a way over, reducing the lead to three, but Australia held on.
Eddie Jones, the former Australia and England head coach, is in his second stint in charge of Japan.
"We let ourselves down with a few fundamental errors in the last 20 minutes when we had an opportunity to probably put Australia away, so pretty disappointed, mate," said Jones.
"But yeah, I'm really proud of how hard the players are playing and there's a lot of development in this team."
