Captain Charlotte Edwards was the star of the show with an England record 92 not out from 59 balls.
The Southern Stars, buoyed by two straight one-day wins, had won the toss and made 150-3.
However Edwards’ knock and an unbeaten stand of 114 with Sarah Taylor (50 not out) saw the tourists ease to 151-1.
The win means England are 10-4 up in the series with two T20 games remaining, an unassailable lead.
Australia’s stand-in skipper, 21-year-old Meg Lanning, said the remaining matches in Melbourne and Sydney would be a chance to begin preparations for Bangladesh.
“We’ve got a T20 World Cup coming up in a couple of months’ time,” she said.
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