Needing 130 to win from 12 overs, Australia were 30-3 from 3.5 overs when rain forced the players from the field for the third and final time.
England captain Jos Buttler said his team was building up well to the T20 World Cup, after winning the three-match series 2-0.
“We made some good strides in Pakistan and we came here (Australia) and continued that form,” Buttler said.
It was a disappointing end to the match, the last official game for both teams before the World Cup, which starts on October 22.
After being sent in by Australian captain Aaron Finch, Buttler smashed 65 from only 41 balls as England reached 112-2 in their 12 overs.
Australia, already 2-0 down in the three-match series, then needed 130 to win based on the Duckworth-Lewis method.
Match abandoned in Canberra.We win the series 2-0!🇦🇺 #AUSvENG 🏴 https://t.co/wU95GcMkVd
— England Cricket (@englandcricket) 1665746784000
And they got the worst possible start when Chris Woakes had Finch and number three Mitchell Marsh caught with the first two balls of the match to stun the home side.
He then dismissed Glenn Maxwell in the third over to leave the Australians in huge trouble at 17-3, before rain forced an early end.
Finch earlier won the toss and chose to field, with Australia getting away to the perfect start themselves, as Josh Hazlewood had Alex Hales caught at first slip in just the second over.
Buttler and Dawid Malan looked comfortable and after a slow start began to accelerate, but shortly after the first rain delay Malan miscued an attempted slog off Pat Cummins and was caught at mid-off by Marsh for 23.
A second rain delay saw the match shortened to 12 overs each, and Buttler came out firing, blasting 22 runs off the 11th over to help set a challenging total.
Woakes’ brilliant opening spell made that target unlikely and an Australian defeat appeared to be saved by the rain.
“It was really hard to stop the (English batters) and credit to them, they outplayed us,” Finch said.