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.
Earlier, Sri Lanka's batsmen scored just 56 runs in the first 10 overs but came back strongly, smashing 105 in the second half of their innings.
Spinners Maxwell (1-23) and Xavier Doherty (1-30) and paceman James Faulkner (1-24) took a wicket each as Australia made inroads into Sri Lanka's batting order.
But Mahela Jayawardene (61 not out off 45 balls), Jeevan Mendis (35 not out from 15) and Perera (25 off 24) ensured Australia faced a difficult run chase.
Sri Lanka's late flurry yielded 80 runs from the final seven overs.
It started when Jayawardene lifted Maxwell for a straight six that remarkably rebounded off a seat and rolled all the way back to the bowler.
And by the closing overs Jayawardene was flourishing in a 59-run partnership with Perera.
The pair clubbed 20 from Ben Laughlin's final over, including three fours and a six, as Australia again closed out their bowling innings poorly.
Laughlin finished with the untidy figures of 1-40 while Mitchell Starc (0-35) also copped late punishment.
The result means Australia have just 30 wins from 60 Twenty20 Internationals.
Worryingly, their top order again failed to fire as Aaron Finch and David Warner were both out for seven.
The match ended on a sour note as Perera and Warner started an argument. Jayawardene and Matthew Wade then took over before Bailey intervened to bring a halt to discussions.
Brief scores
Sri Lanka 4 for 161 (Jayawardene 61*, T Perera 35*)
Australia 3 for 119 (Marsh 47*, Bailey 45)
Result Sri Lanka won by 2 runs (D/L method)
MOM Thissara Parera (Sri Lanka)
