Perry smashed a career-high 90 from 95 balls as the Southern Stars chased down the biggest total of the series to win with three balls to spare on Sunday.
The Ashes looked gone when Australia were 6-199 chasing 269 to keep the series alive but Perry and Erin Osborne (40 from 25) put on 70 to steer their side to victory.
They brought up their 50-partnership off just 31 balls and powered home, celebrating wildly when Osborne steered a ball to he third-man boundary.
The Stars still need to win all three Twenty20 matches in the multi-format series to regain the women's Ashes trophy lost last year in the UK.
Alex Blackwell chipped in with 51 from 75, while England's all-time leading wicket-taker Jenny Gunn took 3-53.
Australia's chase began well when in-form opener Nicole Bolton (31 from 54) put on 57 with skipper Meg Lanning (40 from 30).
Lanning smashed seven boundaries and a six before she was stumped, and when Jess Cameron (5 from 6) was unluckily run out off a ricochet from the bowler it was 2-64.
Bolton, who became the first Australian woman to make a hundred on ODI debut last week, went at 3-81 before Blackwell and Perry put on 88 in a promising rescue mission.
Blackwell was bowled soon after making her 50, the Stars losing 3-30 before Perry and Osborne came together.
Earlier, Sarah Taylor had top-scored for the tourists with 64 (57), with opener Heather Knight making 57 (82) in England's 4-268.
The wickets were shared between Jess Jonassen (1-50), Osborne (1-52) and Perry (1-61), but all proved expensive.
England took six points in the series with their Test win and another two with victory in the first ODI.
Australia have four points from two ODI wins and can claim another six in the T20 matches to regain the Ashes.