Joe Root led the way with a nerveless all-round display as England ran out winners by four wickets with 34 balls to spare.
The win puts them 2-0 up in the five-match series and showed once again that in this format of the game England are way ahead of the world champions.
Australia got their selection wrong by leaving out the leg-spinner Adam Zampa to bolster their batting while Eoin Morgan’s clever captaincy seized the advantage on an untypically spin-friendly Brisbane pitch.
A second successive century from Aaron Finch set the platform for Australia but just as they did in Melbourne, they lost key wickets in clusters.
They managed only 67 runs in the last 10 overs and captain Steve Smith was forced to admit: “Everything fell to pieces again and 270 isn’t good enough against a quality batting line-up like England.”
Root was as surprised as anyone when he came on to bowl in the 20th over after eight overs of more mainstream spin from Moeen Ali and Adil Rashid.
But he took the wicket of Steve Smith with his fourth ball – despite Smith’s desperate review of the lbw – and soon after caught and bowled Travis Head, who looked out of his depth.
Root said: “Eoin just turned to me to try and sneak a few extra overs in – it went a little better than we all anticipated.
“It was quite smart captaincy from him to be able to juggle things round. It’s important to try and give Morgs a few extra bowling options at the death.”
Smith admitted: “I didn’t think we played him as well as we could have done. There were probably a few soft dismissals and it wasn’t as easy as it can normally be playing spin out here.
“Their spinners were getting the ball to stop in the wicket and it was quite hard to hit the line. He bowled really well, great lengths, not much width and was looking to hit the stumps. He did all the things you want a spinner to do.”
Despite losing Jason Roy cheaply, Jonny Bairstow and Alex Hales set England well on the way to victory with a century stand for the second wicket.
Hales, who lost his opener’s slot last September after his part in the infamous Bristol night out, looked in good touch to reach his first fifty for England since last June and his first ODI half-century against Australia.
Both fell to debutant quick Jhye Richardson, who was the only bowler to provide support for the peerless Mitchell Starc, who took 4-59.
Without Starc, England’s win would have been even easier and if he had had just one more over, the result might have been different.
But Root played his second perfectly-pitched finisher’s role in the space of a few days, adding an unbeaten 46 to his 91 not out from Melbourne. He was ably assisted by Chris Woakes, who showed nerves of steel and considerable invention for his unbeaten 39 off 27 balls.
Root said: “It’s a great driver coming from a difficult series like we have. To play convincingly and be there at the end is the sort of thing you pride yourself on as a batter – making sure you’re the one to get the job done.”
He also insisted the continuing uncertainty over Ben Stokes’ return was not a distraction, saying: “It’s out of our hands. We’ve got to make sure we keep trying to win this series and get the best out of this squad.
“When you’ve got guys like Ben still to come back in it’s a great place to be as a side. There’s will be some difficult decisions for Trevor Bayliss and Morgs down the line.”