The tourists chased down the Southern Stars' 3-150 with 13 balls to spare, skipper Charlotte Edwards starring with an England record 92 not out from 59 balls.
Edwards finished it with a boundary, sparking wild celebrations from her teammates.
Australia needed to win the opening T20 match to keep the multi-format series alive but, after hopes were raised by two straight one-day wins, England retained the Ashes they won back at home last year.
The tourists go into the final two T20 fixtures with an unassailable 10-4 points advantage.
They grabbed six points with their victory in the Test and two each from a one-day and T20 win.
Australia's four points come from their two one-day victories.
Stand-in skipper Meg Lanning's highest T20 international score, an unbeaten 78 from 54 balls, helped the Stars to a competitive score.
The 21-year-old, who became the youngest woman or man to captain an Australian cricket team this series, cracked nine boundaries and a six.
Lanning bettered her previous best of 76 against New Zealand last year, her score third behind Karen Rolton's 96no against England in 2005 and Alyssa Healy's 90 against India in 2012.
But opposite number Edwards was unstoppable, getting her side off to a flyer and smashing 14 boundaries and a six in the fourth-highest score by a woman in a T20 international.
She was supported by Sarah Taylor, who made 50 not out from 37 balls.
Australian wicketkeeper Healy will rue the ninth over, when she missed a leg-side stumping and then a potential run out of Taylor.
Australia again went into the match without regular captain Jodie Fields, who continues her recovery from a broken hand.
The two sides meet again in Melbourne on Friday and Sydney on Sunday.