Tries by Jordan Petaia, speedy winger Mark Nawaqanitawase and a double five-pointer by man of the match Ben Donaldson, who kicked the rest of the points, were enough for the two-time world champions to win their first match of the year and end a five-test losing streak - and claim a bonus point.
Georgia, who sprang into action only after the break and wasted several chances, scored two tries through Luka Ivanishvili and Tengizi Zamtaradze with Luka Matkava slotting in an early penalty and Tedo Abzhandadze adding a conversion.
Donaldson, a surprise selection brought into the side primarily for his place-kicking, added 15 points from the tee with three penalties and three conversions, missing just one kick from wide out.
"The boys just executed really for the full 80 minutes and in the end it made me look half decent," said Donaldson.
"I think some of their reserves came in and really brought it to us, we became a bit slow in the second half but I'm proud of the boys."
Georgia, hoping to add another top tier victim to their tally after wins over Italy and Wales in the last 13 months, battled to the bitter end and scored tries through Luka Ivanishvili and Beka Gigashvili.
Although the Stade de France atmosphere was always going to be subdued compared to Friday's opening night party when the hosts beat the All Blacks, Australia contributed by quickly stifling any chance of the upset the majority of the 75,770 crowd wanted.
Centre Petaia wriggled across the line in the second minute and made the break to send winger Nawaqanitawase in for another try seven minutes later before Donaldson took over from the kicking tee to keep the scoreboard ticking over.
The Georgians, pinned into their own half by the Australian kicking, were becoming frustrated and left winger Mirian Modebadze was shown a yellow card just before halftime.
The Lelos came out with renewed purpose after the break and, still down to 14 men, cut the deficit to 21-8 when flyhalf Luka Matkava fired a looping pass out to flanker Ivanishvili on the left wing.
Georgia fullback Davit Niniashvili finally got room to run in the 56th minute but his wild pass backwards found only Taniela Tupou and the Australia prop's neat offload sent Donaldson over for his first try.
Australia were still struggling to find their tempo in the stifling heat but flyhalf Carter Gordon summoned up a superb long pass to allow Donaldson to skip through a big gap and secure the bonus point.
The Georgians kept battling but Nawaqanitawase produced a stunning try-saving tackle to deny winger Akaki Tabutsadze before replacement prop Gigashvili bulldozed his way over from close range in the dying seconds.
