Glenn Maxwell hit two successive boundaries to bring Australia agonisingly close to their target but could not make contact with the last delivery sent down by Thisara Perera as Sri Lanka eked out a narrow victory via the Duckworth-Lewis method.
Put into bat, Mahela Jayawardene (61 not out) featured in fifty-plus partnerships with Jeevan Mendis (25) and Perera (35 not out) to help Sri Lanka overcome a slow start and post 161-4 at the Melbourne Cricket Ground.
Australia lost both their openers cheaply but captain George Bailey (45) and Shaun Marsh (47 not out) guided them to 60-2 in 10 overs before rain led to the loss of five overs' play.
Australia were required to score 122 runs from 15 overs under the revised target and 18 runs from the last over from Perera, who removed Bailey with the second ball and followed it with a waist-high full toss which was adjudged a no-ball.
Marsh managed a single off the next delivery and watched from the other end as Maxwell hit two straight boundaries to raise hopes of a memorable victory before failing to put bat to the ball at the death.