Visiting Sri Lanka opened the batting and managed to record a score of 161-4 from their permitted 20 overs.
Mahela Jayawardene was his country's top scorer, producing an unbeaten knock of 61 runs from 45 balls.
Rain meant that Australia's reply was restricted to 15 overs, which in turn meant that they needed 121 runs to win the encounter under the Duckworth Lewis ruling.
Shaun Marsh (47) and George Bailey (45) took the Aussies into contention as the match went down the final delivery. The hosts required four runs to win, but Glenn Maxwell failed to make a connection and only a single was possible.
The result means that Sri Lanka have taken an unassailable 2-0 lead in a three-match series.