Georgia did not relent under pressure and clawed their way back with a 71st minute try from Sandro Todua but Australia closed the game well with back to back tries from Jack Dempsey and Will Genia in the final five minutes and despite To'omua missing both the conversions, Cheika's men sealed a 27-8 bonus point victory.
The Wallabies lost number eight Isi Naisarani to the sin bin for catching Giorgi Nemsadze with a swinging arm before Toomua's penalty gave them a 10-3 lead at the break. The Lelos have never beaten a Tier One team.
Georgia, which has beaten only Uruguay, is trying to win two pool matches for only the second time, and claim third place from Fiji and an automatic qualifying spot for the 2023 tournament in France.
The Georgians repelled wave after wave of attack, notching up nearly 80 tackles in the first 20 minutes.
Australia have been criticised for their indiscipline in this tournament and it surfaced once again here, Tolu Latu's high tackle awarding Georgia a penalty, with Soso Matiashvili splitting the posts.
There was a lengthy delay while Georgia scrum-half Gela Aprasidze was treated before being carted off with what appeared to be a neck injury after a scrappy start to the second half.
Kurtley Beale was replaced by Dane Haylett-Petty only 13 minutes in after taking a blow to the head in a tackle and Georgia defended magnificently as Australia went through the phases scenting an opening try.
"It was a tough old game", said Australia captain David Pocock.
There was no shock for Georgia, but it was certainly not down to a lack of hunger and commitment.
"Their defence was really solid". Throughout the whole game, they were very solid.
But it was an attritional game in the first ever Test match between the two sides, and a game from which there is plenty to learn from. The Wallabies were desperate to get the first points on the board with Georgia looking good on defence until the 22nd minute when Nic White touched down after a build up from Matt To'omua. "So we'll definitely need to put that on and we'll be ready to take the opportunities next week".
Georgia may be going home, but it leaves Japan with its dignity firmly intact.
"Australia have had a lot of hard games and they have had to work for a lot of their wins".
And although Georgia couldn't finish with a win, its performance against Australia earned it many plaudits.
"We fought well", the centre said. We could have stepped up a played a bit flatter. "We did the country proud".
"Sometimes we have, sometimes we haven't".
"Our first game against Georgia, they certainly delivered in terms of set piece physicality and it was a ideal day for set piece play", Australia captain David Pocock said.