Australia earlier won the toss and chose to bat, but apart from opener David Warner they found scoring difficult.
The Sri Lankans always had the target well in hand, once openers Kushal Perera (33) and Tillakaratne Dilshan (16) put on 46 runs in 38 balls for the opening wicket.
Kushal, making his international T20 debut, showed no signs of nerves as he took to the Australians with relish.
He outscored Dilshan, who was hit in the head by a Ben Laughlin bouncer and needed treatment for a cut above his eye.
Australia finally got the breakthrough when Dilshan fell to the spin bowling of Doherty, Laughlin taking a magnificent diving catch at point.
They struck again soon after when ushal edged Maxwell to wicketkeeper Matthew Wade and Chandimal (5) was caught in the outfield by Ben Cutting off Maxwell.
Doherty then got the wicket of Mahela Jaywardene when he bowled the former Sri Lankan skipper for just eight.
Angelo Mathews (35 not out) and Lahiru Thirimanne steadied the innings and got Sri Lanka back on track but on 104 Thirimanne slashed at a Mitchell Starc delivery outside off stump and was caught at backward point by Adam Voges.
However, Mathews kept the scoreboard ticking over to move the Sri Lankans to within striking distance.
Earlier, Warner played a lone hand with 90 runs off just 62 balls, blasting five fours and three huge sixes. Voges was the next highest scorer with 25, while Kulasekara was the pick of the bowlers with 1-21 from his four overs.
Warne, the brutal lefthander, showed there was a big gap from international cricket to the Big Bash by scoring 90 not out of Australia's 3/137 before 40,000 fans at ANZ Stadium.
