Captain Eoin Morgan smashed a superb 74 off 39 deliveries to lift the home team to 182 for five and despite a brilliant 90 by Australia skipper Steve Smith, the touring side fell just short of their target.
"It was brilliant, a great game of cricket to win," Morgan told Sky Sports. "You can learn a lot from playing in close games against top opposition."
He shared a third-wicket stand of 135 with Moeen Ali (72 not out) after Smith had won the toss and England openers Alex Hales and Jason Roy fell cheaply.
Morgan struck seven sixes and three fours and Moeen hit three sixes and six fours to put England on course for a total in excess of 200.
But quick bowlers Pat Cummins and Mitchell Starc slowed down the run-rate in the closing overs to keep Australia in the game.
Australia openers David Warner and Shane Watson then failed but Smith and Glenn Maxwell put together a fluent partnership.
Maxwell was brilliantly caught by Ben Stokes off man-of-the-match Moeen for 44, the all-rounder running round from long-on to end a third-wicket stand of 112.
"Ben Stokes' catch changed the momentum of the game because the wicket meant it was difficult for a new batsman to come in and score quickly," Morgan said.
Smith made his 90 off 53 balls, including four sixes, but he was caught by Sam Billings off David Willey in the 19th over and Stokes conceded just six runs off the last six balls to leave Australia stranded on 177 for eight.
"It was impressive the way Ben Stokes bowled that final over and delivered his skills after just finishing a five-game test series," Morgan said.
"He stuck his chest out and bowled very well."
Smith was left to rue his team's inconsistent bowling.
"It was one of those games," he said.
"Similar innings from both teams. At the end England were able to hit a few more boundaries which made the difference. We were hot and cold with the ball but credit to Eoin and Moeen."
The teams start a five-match one-day international series in Southampton on Thursday.
(Reporting by Ed Osmond; Editing by Tony Jimenez)
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