After being put in to bat, India's openers Abhishek Sharma and Shubman Gill made a bright start to the innings by putting on 52 without loss in just under five overs before the match was stopped, initially for lightning.
Gill took the early initiative and pummelled six fours in his 29 not out, while his partner Abhishek was dropped by Glenn Maxwell and Ben Dwarshuis on his way to an unbeaten 23.
The sellout crowd at the Gabba hung around optimistically waiting for play to resume, but the stormy weather persisted and the match was abandoned some two-and-a-half hours after it started.
The opening match in the series in Canberra was also washed out before Australia won the second in Melbourne by four wickets on the back of the bowling of paceman Josh Hazlewood.
Australia withdrew Hazlewood and a number of other players named in the Ashes squad so they could prepare to face England with the red ball and India won the third T20 by five wickets in Hobart and the fourth on the Gold Coast by 48 runs.
Abhishek was named Player of the Series for his 163 runs at an average of 40.75.
"The way everybody chipped in in every game and we came back from being one match down, I think credit goes to all the boys; a complete team effort," said Yadav.
India, who top the ICC rankings in the shortest format, will head home with confidence and plenty of player options ahead of their defence of the T20 World Cup title on home soil early next year.
"I thought all in all it was a good series, two teams really going at it," said Australia captain Mitch Marsh.
"India won the games when it mattered so congratulations to them."