The host's 56-17 triumph was in the balance until midway through the second half, when the 1000th Wallaby, Massimo De Lutiis, subbed on and stormed over for a debut try to create an 18-point lead.
It was one of six tries from Australian front-rowers on Saturday and - after a three-point win in Osaka seven days earlier - was the welcome breathing room coach Les Kiss was searching for in his second game in charge.
The impressive Tupou barged over for two close-range tries in the first half while Angus Bell added one, hooker Josh Nasser opened the scoring and his replacement Brandon Paenga-Amosa finished the job.
Japan coach Jones said it was the Wallabies' aerial dominance and subsequent possession that turned the tide, acknowledging in his own colourful way the force of Tupou.
"He must have thought there was a free pizza every time he scored a try today; I'll have to go and see him after the game, might take him a pizza in," Jones said.
"They (Wallabies forwards) get pretty excited near the line."
Carter Gordon controlled play nicely in his return at flyhalf while halfback Ryan Lonegan (5/5) was perfect off the tee.
Unforced errors kept Japan in it through the first half and the visitors led 17-14 before Tupou snuck in his second try before halftime to trigger a run of 42 consecutive points.
Slowly the hosts turned the screws, Carlo Tizzano pilfering three times and Fraser McReight immediately adding a steal when he came on in the final 15 minutes.
The Reds flanker replaced cramping lock Lachlan Shaw, who held the lineout together in his starting debut, teaming with fellow pilferer Tizzano and shifting Harry Wilson into the second row.
That finally broke the Japan resistance, with backrowers Charlie Cale and Harry Wilson getting on the board before Paenga-Amosa's after-the-buzzer effort.
"Test rugby, sometimes it takes a while to break a game down," Kiss said, crediting his assistants for the side's effectiveness close to the line.
'"We gave them (Japan) a bit of scope to be able to play their quite fast and furious game but we were cool, calm and collected (at half time).
"We just made sure we got the right things right."
Isaac Henry was impressive in his second Test and first start in the No.13, replacing the injured Joseph-Aukuso Suaalii to give Kiss food for though ahead of a two-Test tour of Argentina.
Henry's straight running busted the line regularly, with his assist for Lonergan waved away due to an earlier forward pass.
It was mission accomplished for Kiss, who avoided two banana-peel clashes against the side that dropped from 10 to 12 in the world last week.
And his selections, explained as "future-proofing" were also validated after in-form lock Josh Canham and prop Allan Alaalatoa were both rested in Townsville.
"We need to create this competitive pressure but also create the flexibility that players can adapt and move into different positions," Kiss said, pointing out that Suaalii had shifted to wing to finish last week's Osaka Test.
Kiss also lauded De Lutiis's "dream" debut, forged on hard work, and said only some injury concerns meant McReight didn't come on earlier to partner Tizzano.
"McZzano," Kiss chuckled of the nickname that plays on the "Pooper" combination of Michael Hooper and David Pocock of a decade ago.
"I would have liked another five minutes of that, but at least we saw it as a snapshot.
"Just trying to build ways that we can think forward, and the different plans that we might be able to play against a different opposition."
Winger Max Jorgensen left the field nursing his ribs after some friendly fire with Wilson in the only apparent injury concern.
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