Young guns Freddie Steward and Marcus Smith scored the tries and England's streetwise pack bossed the breakdown as coach Eddie Jones masterminded a second series victory over his own country after their 3-0 sweep in 2016.
Australia scored tries through Tom Wright and Folau Fainga'a in front of a sellout crowd of 43,274 at the Sydney Cricket Ground, but the home side's accuracy deserted them too frequently at crucial moments.
Australia won the opening test 30-28 in Perth but England struck back with a 25-17 victory in Brisbane to take the series to Saturday's decider.