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.
"There is a real feeling this team could do something," Eddie Jones said after the first victory of his second reign as Australia coach.
"We've got a young team, it's a great learning experience for them.
Georgia never looked like adding another top tier victim to their tally after wins over Italy and Wales in the last 13 months but battled to the bitter end and scored tries through Luka Ivanishvili and Beka Gigashvili.
Australia head south for their second Pool C match in St Etienne on Sunday against a dangerous Fiji side who recently beat England.
Persons:
Australia's Ben Donaldson, Livewire, Mark Nawaqanitawase, Jordan Petaia, Donaldson, Eddie Jones, We've, it's, Luka, Nawaqanitawase, Mirian Modebadze, flyhalf Luka Matkava, Davit Niniashvili, Taniela Tupou, flyhalf Carter Gordon, Akaki Tabutsadze, Gigashvili, Levan Maisashvili, Nick Mulvenney, Hugh Lawson, Ed Osmond
Organizations:
Georgia, Wallabies, Stade de France, Luka Ivanishvili, Blacks, Australia, Petaia, Georgians, flyhalf, Australians, Portugal, Sunday, England, Thomson
Locations:
Australia, Georgia, Italy, Wales, St Etienne, Fiji