Nuwan Kulasekara was Australia's tormentor-in-chief, removing four of the hosts' top five on his way to figures of five for 22 as Australia capitulated to 40 for nine, before scrambling to 74.
That edged them past their lowest-ever total of 70, scored against England in 1977 and New Zealand in 1986, as Mitchell Starc (22no) and Xavier Doherty (15) added 34 for the last wicket. Mitchell Johnson (three for 11) then reduced the tourists to 37 for four but they eventually limped to 75 for six off 20 overs and lead the five-match series 2-1.
Australia opener David Warner scooped an Angelo Mathews delivery to Shaminda Eranga at mid-off in the third over, and Kulasekara saw off Phil Hughes in his third over, before claiming David Hussey (four) and George Bailey for a duck with consecutive deliveries in his fourth.
The unplayable Kulasekara was not done yet, though, clean bowling both Michael Clarke (nine) and Moises Henriques (two) in the 12th over to leave the Aussies reeling at 30 for six.
Lasith Malinga (three for 14) chipped in with the wickets of Johnson (two), Matthew Wade (eight) and Clint McKay (three) to stifle any notions of an Australia fightback.
Ironic cheers rang around the Gabba as Australia passed 50 in the 22nd over before Doherty was eventually dismissed by Eranga (one for 12) to end a dismal batting performance.
Sri Lanka made a poor start to the run chase, losing Mahela Jayawardene in the first over, brilliantly caught at point by Warner off McKay, but it was the introduction of Johnson in the 10th over that had them rocking.
The left-armer took the bizarre wicket of Tillakaratne Dilshan (22) with his third ball, the opener trying to withdraw his bat but only steering the ball to Clarke at slip. In his next over, Lahiru Thirimanne slashed straight to Warner at point and Mathews then went first ball.
Starc had Upul Tharanga caught at slip by Clarke but Kushal Perera took six off the next over to take his side within six of victory. Jeevan Mendis was dropped by the usually reliable Warner, although he was dismissed soon after, while Thisara Perera struck the winning boundary.
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