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.
