Fired by half-centuries from captain and man-of-the-match Mahela Jayawardene and Dinesh Chandimal, the tourists were ushered to victory by a brilliant cameo from all-rounder Thisara Perera who blasted an unbeaten 21 off 11 balls in the final few overs.
Perera smacked a six and a four in consecutive balls to leave his team needing only three runs from the final over and paceman Nuwan Kulasekara bashed a boundary through the covers to bring up the winning runs.
The victory continued Sri Lanka's stunning turnaround in the series, which also includes India, after they went winless from their first three matches.
Australia captain Michael Clarke won the toss and elected to bat in glorious sunshine on a flat pitch at Bellerive Oval, and enjoyed a 154-run stand with Peter Forrest after openers Matt Wade and Dave Warner both fell cheaply.
Forrest, promoted to three after former skipper Ricky Ponting was dropped from the side earlier this week, marked his fourth one-day match with a glittering 104.
The 26-year-old New South Welshman blasted two sixes and 10 boundaries in his 138-ball knock before his post-century celebrations ended quickly at the hands of Angelo Mathews.
Deceived by a slower ball, Forrest attempted to slog over the covers, but succeeded only in skying a simple catch to Farveez Maharoof.
Mathews also removed Clarke for 72 two overs prior to Forrest's dismissal, the Australia captain slogging over midwicket to Thisara Perera, who took a brilliant catch just above the grass after sprinting from the boundary.
Mike and Dave Hussey combined for a quick-fire 42-run stand but paceman Lasith Malinga took the wind from Australia's sails when he bowled the former for 21 with a sizzling yorker.
Allrounder Dan Christian was stumped for six after charging down the wicket to meet spinner Rangana Herath, and Australia managed only 30 runs from their last five overs to give the tourists hope of reeling in the total.
Sparked by a belligerent Jayawardene, Sri Lanka marched to 51 in eight overs before Tillakaratne Dilshan was out for three, pulling a Ben Hilfenhaus delivery straight to Forrest at deep square leg.
The Sri Lankan captain marched on with a 45-run stand with wicketkeeper Kumar Sangakkara, who fell for 22, poking an edge to Warner at backward point off an innocuous delivery from Christian.
Jayawardene added another 49 with Dinesh Chandimal before being stumped, deceived by a venomous, turning ball from spinner Xavier Doherty.
Chandimal's 80 drove Sri Lanka to 243-5 before he was trapped in front by paceman Ryan Harris, who caught Maharoof for five off the bowling of Ben Hilfenhaus in the following over.
Mathews was out for 24, slogging a rash shot straight to Dave Warner in the deep to give the hosts their seventh wicket and briefly raise their hope of stopping the Sri Lankan charge.
But with 14 runs needed from the last nine balls, Perera plundered two short balls from Christian for 10 runs to propel the tourists to victory.
