The Red Rose picked up their 21st victory in 22 matches under Jones by crossing over four times at Twickenham Stadium in a record 30-6 win, courtesy of Elliot Daly, Jonathan Joseph, Jonny May and Danny Care.
Three calls via the television match official system went in England's favour, which left opposition boss Michael Cheika "confused", but a delighted Jones - who is now preparing his side to take on Samoa next week in their third and final Autumn International - is adamant that each decision was correct.
"Why do we have referees? Why do we have television match officials? They do 10 replays of the video and they make a decision," he told reporters. "How are we lucky? We had the bounce of the ball otherwise Jonny May would not have scored his try, but that has nothing to do with the referee or the TMO.
"We will sit down and decide whether to make changes or stick with this side and see if we can play better [against Samoa]. It was a tough old game against Australia, a great Test between two even teams. It was an arm-wrestle and we stuck at it.
"You had to take your opportunities and we did that better than them, smart tactically in really difficult conditions which we played superbly."
Victory for England consolidates their position as second in the world rankings behind New Zealand.