Loose-forward Hamish Watson also crossed for a try, and flyhalf Finn Russell slotted one penalty and a conversion as the Scots kept up their winning run against Australia with a third successive victory.
Australia, who were beaten at the breakdown and in the scrum, managed a single try through loose-forward Rob Leota as prop Allan Alaalatoa also received a contested yellow card.
Russell landed the winning penalty after 69 minutes as the visitors were penalised at the scrum yet again, much to the delight of the home fans in the 65,700 crowd.
Meanwhile Wallabies' fullback Dane Haylett-Petty announced his retirement after failing to fully recover from the effects of a concussion he suffered last year in a match against the All Blacks.
The concussion, in a collision during a Bledisloe Cup match in October 2020, left Haylett-Petty with lingering headaches. It ruled him out of the 2021 Super Rugby season with the Melbourne Rebels, where he was the team's skipper.
The 32-year-old, who has not played for the Wallabies since the injury, finishes his career with 38 test caps.