Sri Lanka captain Mahela Jayawardene elected to field first and the move paid off as they bowled Australia out for just 170.
The run chase was then in cruise control thanks to a 137-run second wicket partnership between Tillakaratne Dilshan and Thirimanne as Sri Lanka cruised to 2-172 with eight wickets and 59 balls in hand.
Sri Lanka did lose the early wicket of Upul Tharanga for a first over duck when he was caught behind off Clint McKay, but Dilshan and Thirimanne steadied the ship nicely.
It was slow going early on in the partnership, but the pair knew that the total wasn’t a big one and did exactly as was required.
Even though Dilshan did fall to Ben Cutting for 51, the score by that stage was 2-137 and Sri Lanka was well on top. Thirimanne went on to score his maiden international century after previously playing eight Tests and 32 one-day matches for Sri Lanka.
He remained 102 not out from 134 balls with 12 fours and Thisara Perera offered good support at the end with 14 from 16.
On top of the loss, there was further bad news for Australia with wicket-keeper Brad Haddin, fresh off top-scoring with 50, going off with a hamstring injury in the 19th over of Sri Lanka's innings.
Earlier, after falling to 2-12, 3-51, 4-60 and 6-83, Australia did reasonably well to end up with 170 largely thanks to a 50 from Haddin before being bowled out in 46.5 overs.
Lasith Malinga claimed 3-32 from nine overs for Sri Lanka with Thisara Perera taking 2-40, Angelo Mathews 2-24, Nuwan Kulasekara 1-24 and Ajantha Mendis 1-41.
Play was delayed for around an hour due to some slight wetness in the outfield, but Jayawardene did not hesitate to bowl first when he won the toss and so far the move has paid off for Sri Lanka.
Coming off a 3-0 Test series loss to Australia and then going down by 107 runs in the first one-day clash at the MCG on Friday, Sri Lanka needed a confidence-boost and would have got it from their bowling effort.
Australia opened up with Friday's debutants Aaron Finch and Phil Hughes, but the pair both fell early with Finch the first to go for four when he was caught by Jeevan Mendis off Mathews.
The Australians were then 2-12 after seven overs when Kulasekara trapped Friday's centurion Hughes for three. Hughes did review the decision, but the ball from Kulasekara pitched in line with leg stump and it showed it was cannoning into the middle of middle and leg.
Australian captain George Bailey and Hussey then led somewhat of a rescue mission, but it proved to be short-lived with Bailey out for 26 when Thirimanne took an outstanding catch at mid-wicket off Malinga.
Hussey was then joined at the crease by Smith, who came into the side to replace Usman Khawaja. That was one of three changes made by Australia with Mitchell Johnson and Mitchell Starc also out for debutant pair Kane Richardson and Cutting.
Smith didn’t last long, out for eight when he was caught behind off Perera and then Glenn Maxwell looked all at sea in his eight before also being caught behind off Mathews.
Australia was then 6-83 but Haddin was joined Cutting and the pair did well to combine for a 57-run stand with Cutting making 27 on debut from 45 balls before being caught behind off Malinga.
Haddin did end up making his 50 from 67 deliveries with four boundaries and a six, but Richardson (0), McKay (4) and Xavier Doherty (5 not out) offered little support with the home side bowled out for 170.