Australia coach Eddie Jones was able to celebrate a first Twickenham win after another close encounter with England. "We have lost some close games here in the last few years so it is nice to win one," Jones said.
"We stuck at it, showed great character and played exceptionally well to hang on in that second half.
"After the defeat against France there had been a bit of introspection in the squad but we shifted the ball around and caused them a lot of problems."
Jones singled out centre Matt Giteau - who switched to fly-half after Elton Flatley went off injured in the 24th minute - for special praise.
"He's worked hard at his game and his goal-kicking stats are more than 80% on this tour," Jones added. "He is a very talented player with a great future and number 10 suits him physically.
"We feel we have developed a good team on this tour. It has been a purposeful month for us. We've got stuck in after the French defeat and solved a lot of problems. Today we had the courage to keep playing the way we wanted to play."
Full-back Chris Latham, who scored Australia's second try, was named man-of-the-match after a superb all-round display.
"That was one of the best games I have ever been involved in," Latham said.
"We should have taken it away from them in the second half but that is a quality England team and they came back at us. "But we dug in well. We knew that we are the best in the world at defence, and when we had the ball we used it well.
"I can't explain how good it feels; it means the world after a tough tour."