But the victory has come at a cost, as middle order batsman Chris Lynn was forced to leave the field after dislocating his right shoulder while attempting a dive.
Short hammered his second T20I half-century in just 29 balls before he was dismissed by Colin Munro, while Warner struck 25 as Ish Sodhi got him bold out.
Ashton Agar, who claimed three wickets in the first innings, did not have a good show with bat and was removed on just 2 as Australia reached 84/3 in 10.3 overs.
Aaron Finch and Glenn Maxwell were batting on 20 and 28 respectively and took Australia to 121 before rain interrupted the play.
The second of two rain interruptions eventually saw the match get called off, with the result being awarded to Australia based on the Duckworth-Lewis method.
In the first innings, New Zealand set a below-par total as they lost wickets in the middle overs.