Australia crossed over three times in an electric opening 20-minute burst and held a decisive 26-10 half-time lead on a clear, but windy afternoon.
They had to fend off a determined rally from Georgia in the second-half before easing to victory in a high-octane match featuring 10 tries.
It continued a perfect start to the tenure of New Zealander Schmidt after Australia won back-to-back Tests earlier this month against Wales.
"The boys are very happy. We probably didn't help ourselves with discipline, but we dug deep," said Allan Alaalatoa, who became the Wallabies' third captain in as many matches.
"You have to give Georgia credit. They never went away and we knew it was going to be a tough physical game."
Underdogs Georgia, ranked 12th in the world, were fresh off a narrow win against Japan in Sendai.
But they rued a slow start and struggled to cope with Australia's speed as scrum-half Tate McDermott repeatedly dashed past Georgia's ragged defence.
"Little mistakes in the first-half cost us, but the second-half was better," said Georgia fly-half Tedo Abzhandadze.
"We tried out best to show the world we can play against a tier-one team. We had opportunities to win, but we didn't take them."
It was just the third time the teams squared off and the first outside a World Cup.
Schmidt continued to experiment for Australia's final match before the Rugby Championship in August, where they will start with back-to-back games against world champions South Africa.
Winger Darby Lancaster made his debut amid 10 changes to the starting line-up.
The Wallabies were wary with most of the Georgians playing at the club level in France, fuelling optimism they can become a top-tier rugby nation.
But in their first match in Australia since the 2003 World Cup, Georgia received a blow when captain Beka Gorgadze did not take his place after collecting a knock against Japan.
Georgia needed to make the most of their opportunities and an accurate penalty kick from Luka Matkava in the second minute eased nerves.
But Australia responded quickly when Hunter Paisami barrelled over for the opening try.
The Samoa-born Paisami provided explosive bursts as tries to Rob Valetini and Isaac Kailea gave Australia a 19-3 lead.
But Georgia hauled back into the contest with a long period of possession and were rewarded when Giorgi Babunashvili barged over the line.
Their comeback was short-lived when Fraser McReight finished off a well-executed set-piece just before half-time.
The Wallabies played with one less player early in the second-half after Filipo Daugunu's yellow card for a clumsy charge was upgraded to red at the interval.
Georgia capitalised with Davit Niniashvili kicked into an opponent, but fortuitously collected the ricochet and jogged under the crossbar.
Akaki Tabutsandze then produced a moment of brilliance when he wrestled possession from Lancaster and sprinted off unopposed under the posts.
But Australia steadied through Valetini and McReight to ensure their winning streak continued.
Alex Hodgman became just the fourth man to represent both New Zealand and Australia in Test rugby, with the substitute loosehead prop taking the field in the second half.
