Buttler's 65 not out off 41 balls helped England to 112-2 after two downpours had reduced the third T20 to 17 and then 12 overs per side, while Ben Stokes was unbeaten on 17 off 10 deliveries.
Australia were set 130 under the Duckworth-Lewis-Stern method but their hopes of a consolation win were hindered as Aaron Finch and Mitchell Marsh were snared by Woakes in the first two balls of the reply.
Woakes had his third by dismissing Glenn Maxwell but, with just seven more balls to get to five overs which would constitute a result, a third deluge proved terminal with Australia in trouble on 30-3.
A no-result means England walk away with a 2-0 win, their first series triumph under Buttler, who hit seven fours and a six on Friday, having been a bystander for the 4-3 victory in Pakistan due to injury.
England will play one official warm-up match against Pakistan in Brisbane on 17 October before getting their T20 World Cup campaign underway against Afghanistan five days later.
Hosts Australia take on India in a warm-up match before opening their tournament against New Zealand in Sydney on 22 October.