After restricting NZ to 150, Australia were well on their way at 121/3 when rain stopped proceedings, and seal final by 19 runs on DLS method.
Pakistan remained the top-ranked side with 0.19 decimal points more than Australia tally of 125.84.
Australia kept winning, and came up against New Zealand in their final fixture, at Auckland on Wednesday.
New Zealand, who beat England by 12 runs in their previous match, advanced to the Feb. 21 final on net run rate.
Morgan returns to the side, knowing they must win by a considerable margin to pip the hosts on net run rate.
Australia scripted history by registering the highest run chase in T20I history as they beat NZ by five wickets in a thrilling game in Eden Park.
The Blackcaps take on unbeaten Australia of the 5th T20I of the tri-nation T20 series in Auckland Friday.
England suffer a third Twenty20 defeat in a row as they are beaten by New Zealand in the tri-series.
Australia are already in the tri-series final. The identity of their opposition will depend on which team can overcame their batting issues.
All-round Australia sweep into tri-series final with seven wicket in over England at MCG on Saturday.
