“The boys are very happy with that,” said Australia skipper Allan Alaalatoa.
“Our discipline didn’t help us and we had to roll our sleeves up, especially with Filipo out for 20 minutes of the game. I’m just very proud of the effort.”
Niniashvili had crossed in the 43rd minute and Aka Tabutsandze added the second five minutes later after a counterattack from behind the Georgian try-line, the right winger gathering his own kick to touch down after running 110 metres.
Valetini soon finished off a move featuring the whole Australia back row; however, McReight scored his second try off a rolling maul to give Australia breathing room before Tabutsandze added another score with a clinical finish in the corner.
Lock Mikheil Babunashvili also crossed in the first half for the Georgians, who had arrived in Sydney looking for an upset after beating Japan last week.
Prop Alex Hodgman, who played four tests for the All Blacks in 2020, came on as a second-half replacement to become the first player in the professional era to represent both New Zealand and Australia.
The Wallabies, who beat Wales twice in their other July tests, will face world champion South Africa in their Rugby Championship opener in Brisbane on August 10.