Two overs were lost due to a rain interruption early in the Australian innings and the target was reduced to 278.
Australia made a rapid-fire start to the run chase with Alyssa Healy and Nicole Bolton producing another fine opening stand to blunt the new ball threat offered by England's Katherine Brunt and Anya Shrubsole.
An unbeaten captain's knock of 88 from Heather Knight has helped England defeat Australia by 20 runs in the final ODI of the womens' Ashes.
The next match in the series is the Test, which begins at North Sydney Oval at 2:30pm on the 9th of November.
"We had to put a good target on the board", England wicketkeeper-batsman Taylor told BBC Test Match Special.
Australia were victorious in the first two ODIs to take a 4-0 lead but England's 20-run Duckworth-Lewis victory at Coffs Harbour on Sunday left the multi-format series in the balance.
"She (Knight) batted really well and would have been a big wicket for us to get, but in saying that our bowlers did really well in that final 10 overs to keep them to 280".
"I'm really proud of the way the bowlers bowled; those middle overs were key".
"It was up to one of me or Nicole to guard the run chase - but we got ourselves out".
Alex Blackwell toiled hard in her innings of 37 in her 250th worldwide match, but the lack of pace from the England bowlers made the going tough, the pressure proving too much for Australia's middle order.
Megan Schutt had been Australia's leading wicket taker in the opening two matches and her good run continued, picking up another four wickets including the scalps of the risky Taylor and Beaumont.
Healy would go on to make her fifty in the 14th over - after smashing Sophie Ecclestone for three boundaries from four balls and a single on the last ball of the over completing the milestone.
Knight had been quietly scoring at a run a ball and she continued that trend, even when Brunt fell to Ashleigh Gardner and Jenny Gunn nicked behind.
She was eventually caught at long-on by Lauren Winfield off Sophie Ecclestone to take Australia to 159-2 in the 30th over, nearly neck and neck with where England had been at the same point.
Spearhead Megan Schutt snared figures of 4-44 but England posted its highest total in an ODI against Australia, surpassing the 3-279 it managed in 60 overs while hosting the 1973 World Cup.
But their departures saw the run rate dwindle, with Rachael Haynes' charges only able to reach 257-9 as England cut their opponents' lead to 4-2 - Alex Hartley scooping 3-45 and Nat Sciver 2-24. Another Australian victory on Sunday would give the hosts a 6-0 points lead, with just a further two required from the remainder of the series to retain the Ashes.
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