The 12th-ranked Georgians threatened a boilover after closing to within two points of the hosts early in the second half before the Wallabies kicked away late at Allianz Stadium on Saturday.
Schmidt made 10 changes to the side that beat Wales 36-28 last Saturday in Melbourne and some seized the opportunity while others didn't.
New flyhalf Ben Donaldson didn't look the answer to Australia's playmaking dilemma, his kicking and decision-making too often poor.
The Wallabies had the tireless back row of Fraser McReight, Rob Valetini and Harry Wilson largely to thank for helping secure three straight wins for the national side for the first time since 2021 when under Dave Rennie.
Fraser McReight scores one of his two tries in a man of the match performance. (James Gourley/AAP PHOTOS)
Lock Nick Frost and first-time starting prop Isaac Kailea were also strong but the first-half dismissal of winger Filipo Daugunu for a dangerous tackle made life difficult for the home side.
Daugunu's initial yellow card for kneeing Georgian winger Demur Tapladze in the head while airborne and trying to charge down a kick was elevated to a red at halftime.
The disruption didn't help Schmidt's new-look outfit as they struggled to put the spirited eastern Europeans away.Still, the Wallabies looked to have the game wrapped up with a 26-10 lead into the break.
After falling behind to a second-minute penalty goal to impressive Georgia five-eighth Luka Matkava, the Wallabies crossed for three tries in 15 minutes through centre Hunter Paisami, Valetini and Kailea.
Then the hosts lost their way.
Ill-discipline and Daugunu's departure invited the eastern Europeans back into the contest as Georgia reduced the deficit to 19-10 with a 33rd-minute converted try to lock Micheil Babunashvili.
Only a driving maul try to man of the match McReight on the stroke of halftime gave the Wallabies some breathing space.
And it didn't last long as Georgia closed to within two points of Australia with two scintillating tries early in the second half through fullback Davit Niniashvili and lightning winger Akaki Tabutsadze.
For all their pluck and resilience, the tide turned back in the Wallabies' favour after Georgia themselves were reduced to 14 men with the sin-binning of Niniashvili for a deliberate knock down as Australia pounded their line.
A McReight break and 40-metre burst set up Valetini's second try and there was no coming back from The Lelos.
McReight completed his own try double to restore Australia's 16-point advantage before Tabutsadze crossed for a consolation second five-pointer late on.
Schmidt, conceding pre-match it was difficult to strike a balance between building depth and winning, will take the victory.
But after Eddie Jones' side downed Georgia by 20 points during last year's ill-fated World Cup campaign, the new coach will also recognise the Wallabies need to improve markedly for their Rugby Championship opener against the top-ranked Springboks in Brisbane on August 10.
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