It followed a 39-28 win in the first Test in Brisbane last weekend to move into an unassailable 2-0 lead in the best-of-three series.
The triumphs have come just eight months after England crashed out as hosts of the 2015 Rugby World Cup in the pool stages, with defeat to Australia sealing its fate.
But under new coach Eddie Jones, who took over from Stuart Lancaster after the global showpiece, England has enjoyed a remarkable turn around in fortunes, first winning the Six Nations title and grand slam and now lifting the Cook Cup Down Under for the first time.
Owen Farrell, switched to inside center by Jones, proved the visiting hero with 18 points from a late try, two conversions and three penalties.
Skipper Dylan Hartley put his side ahead with an early try off a rolling maul, converted by Farrell, who made it 10-0 with a penalty.
Home skipper Stephen Moore crossed for a converted try as England led 10-7 at the half, but magnificent defense ensured there was to be no further scores for the Wallabies.
Late on, Farrell rushed to touch down Jamie George's kick forward for a try under the posts and he rubbed it in further with a penalty on the final buzzer.
Jones praised his side's defense and singled out James Haskell and man of the match and former captain Chris Robshaw for particular praise.
"They are outstanding team men," he said.
"I've never seen a team so pleased for Robbo to get his 50th cap and win man of the match."
His side moves to second in the world rankings behind World Cup winners the New Zealand All Blacks, who earlier Saturday clinched its three Test series over Wales with a 36-22 win in Wellington.
"We want to be the best team in the world," added Jones. We know Australia will come back at us, they are a well-coached, driven team. We are anticipating a feisty encounter in Sydney (for the third Test)."