Australia needed 28 runs from the final two overs, with Hodge (21 not out) and Brad Haddin (four not out) up to the task.
Warner's career-best form made a seamless transition from cricket's longest format to its shortest as he put one ball from debutant Beuran Hendricks out of the park.
In positive signs for Australia leading into the T20 World Cup, Warner offered only the one life on 36 in the third over when Parnell was unable to complete a juggled attempt on the rope.
The Proteas finished 1-80 from their seven overs, Faf Du Plessis (27no) and Quinton de Kock (41no) sharing an unbeaten 74-run stand.
George Bailey opted to field first in the shortened match that featured one-over spells from the visitors' bowlers with the exception of Nathan Coulter-Nile (1-17 from two overs) and Mitchell Starc (0-24 from two overs).
For most of the night it looked unlikely the game would go ahead.
Ground staff worked overtime and liberally dumped large clumps of sawdust on the sodden surface.
Both skippers had long discussions with the umpires and match referee Chris Broad after the showers cleared, no doubt concerned about the risk of injury before this month's T20 World Cup in Bangladesh.
"The final decision lies with them (the umpires)," Proteas captain du Plessis said at the toss.
"It looks ok, so hopefully everything's alright."
- AAP