Half-centuries from Heather Knight (69) and Sarah Taylor (64) ensured England chased down Australia's 203 for four with 16 balls to spare.
Victory was secured when Ellyse Perry slid a wide down leg-side allowing England to go 6-4 points ahead going into the three Twenty20 internationals.
England must win two of those matches to regain the Ashes from Australia.
The home side showed early attacking intent as they plundered eight off the first over, but captain Charlotte Edwards was gone with the first ball of the third.
Alex Blackwell took the catch off an Erin Osbourne (three for 49) delivery and the captain was gone for a run-a-ball eight.
Knight and Taylor soon had England in command as they brought up a century partnership for the second wicket.
Knight brought up her 53-ball half-century in the 18th over and then smashed 11 runs from the 19th as her partner at the crease also brought up her fifty.
Taylor's came in a slightly more swift 48 balls and, while both fell in quick succession, Natalie Sciver's unbeaten 18 got them over the line.
The game was delayed by three hours but when it was decided that a 36-over contest could get under way at 2pm, Australia won the toss and decided to bat.
England got off to a flying start as Alyssa Healy fell for a duck with Dani Hazell claiming a catch off the bowling of Anya Shrubsole with the score on just three.
But the tourists soon steadied the ship and Meg Lanning (64) and Jess Cameron (28) put fifty on for the second wicket before the latter was stumped by Taylor as Hazell claimed her second wicket.
Lanning was playing beautifully and built another partnership as she and Jodie Fields added 67 in just over 11 overs.
The opener was bowled by Holly Colvin in the 25th over after scoring 64 from 69 balls and just nine balls later Fields (27) followed her, this time Taylor taking a catch off Hazell.
With the score at 126 for four with just 10 overs remaining, England would have fancied their chances of seriously limiting the Australian total but Perry and Blackwell had other ideas.
They put on an unbeaten 77 in the remaining overs, with Perry hitting four fours and a six in her 45 while Blackwell added 35 off just 29 balls.
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