Sri Lanka lost just two wickets and reached the revised target of 152 runs in just 24.1 overs to taste their maiden win in the tournament.
Skipper Mahela Jayawardene remained the top scorer for Sri Lanka as he made an unbeaten 61.
At the half stage of the tri-series, India lead the standing with 10 points ahead of Australia (9) and Sri Lanka (7).
Earlier, Sri Lanka came up with a terrific bowling performance to bundle out Australia for 158 runs.
Nuwan Kulasekara ran out Mitchell Starc with a direct hit to end the Australian innings in 40.5 overs.
Waging a lone battle, David Hussey top scored for Australia with a 64-ball 58 that came with the help of six hits to the fence.
Australia lost their eighth wicket when Thisara Perera ran out Brett Lee with a direct hit.
Rangana Herath trapped Clint McKay plumb in front of the wicket as Australia lost their seventh wicket with less than 100 runs on the board.
Nine overs were lost due to rain and the match was reduced to 41 overs.
Australia were down in the dumps at 88/6 in 26 overs when rain stopped play.
Australia lost their sixth wicket when Thisara Perera trapped Dan Christian plumb in front of the wicket.
Farveez Maharoof had Peter Forrest caught by Angelo Mathews in the slips to reduce Australia to 74/5.
Australia lost their fourth wicket when Angelo Mathews had Michael Hussey caught behind by Kumar Sangakkara.
Australia lost stand-in captain Ricky Ponting and opener Matthew Wade in successive overs.
Australia lost their third wicket when Wade was run out after a mix-up Peter Forrest. Wade played a Nuwan Kulasekara delivery into the covers where Thisara Perera dived full length to gather the ball. Forrest was reluctant for the single from the start, but chose to run after Perera stopped it, but Wade had already backed out and both were stranded mid-pitch when Perera lobbed the ball back to Kulasekara to remove the bails.
In the previous over, Farveez Maharoof foxed Ponting by a slower delivery who was early into his flick across the line and ended up chipping it back to the bowler.
Lasith Malinga had David Warner caught by Farveez Maharoof at mid-on off a slower delivery as Australia got off to a bad start.
Malinga choked Warner with unplayable deliveries throughout the over and then bowled a slow delivery as Warner gave the charge but spooned it to Maharoof at mid-on with the clear case of getting undone by the pace.
The breakthrough for Sri Lanka came in the fifth over after stand-in Australian captain Ricky Ponting won the toss and chose to bat.
Australia have brought in Michael Hussey for Michael Clarke and replaced Ryan Harris with Brett Lee.
Sri Lanka have dropped Upul Tharanga for Lahiru Thirimanne and Farveez Maharoof replaces Sachithra Senanayake.
There is a hint of grass on the pitch so there will be good assistance for the seamers in spite of it being a wonderful batting surface. There are thunderstorm predictions in the later part of the day.
With Michael Clarke out nursing a hamstring strain and the selectors not too confident about vice-captain David Warner, Ponting has been handed the job he quit last year.
Australia: Ricky Ponting (Capt.), David Warner, Matthew Wade, Peter Forrest, Michael Hussey, David Hussey, Dan Christian, Brett Lee, Clint McKay, Mitchell Starc, Xavier Doherty.
Sri Lanka: Mahela Jayawardene (Capt.), Tillakaratne Dilshan, Kumar Sangakkara, Dinesh Chandimal, Lahiru Thirumanne, Angelo Mathews, Thisara Perera, Farveez Maharoof, Nuwan Kulasekara, Lasith Malinga, Rangana Herath.