Steward stepped around Kurtley Beale for the opening try in the eighth minute, but England were unable to take full advantage of Australia being reduced to 14 men after Tom Wright was sent to the bin for catching Jamie George in the head with his shoulder.
Only a sublime last-ditch tackle from Nic White stopped George touching in the corner in the 35th minute and O'Connor's fourth successful penalty before Wright returned meant there were just four points in it at the break.
O'Connor closed the gap further after the restart, but Angus Bell was sin-binned for a dangerous tackle on Courtney Lawes and Farrell slotted through the resulting penalty, though he missed another effort from the tee before Bell returned.
An ankle injury forced Hooper off before the hour mark and Farrell put a converted try between the teams with a successful penalty after Bell's scrum infringement.
The game was already put to bed before Noah Lolesio gave the ball away to Sam Simmonds, who teed up Blamire for a try that Marcus Smith converted to make the result look more comfortable.
Eight straight for England
Since Eddie Jones took over, England have been victorious in all of their eight meetings with their coach's home nation. They have never enjoyed a better winning run against the Wallabies, who last got the better of England at the 2015 Rugby World Cup.
Australia still struggle in Europe
Having succumbed to back-to-back defeats against Scotland and England, Australia have now won just two of their past 10 away Tests versus European teams. They will hope to end the skid against Wales at the Principality Stadium next weekend.
