Johnson didn't play because a side strain, forcing Australia to blood two fast bowling first-gamers in Ben Cutting and Kane Richardson, who endured a horror debut.
Richardson made a golden duck and then, after six wicketless overs, was banned from bowling again after receiving a third warning for running on the pitch.
Australia will name its squad for the third and fourth games of the series on Monday, with first-choice gloveman Matthew Wade certain to be recalled.
Haddin, who played the opening two games while Wade was rested, top-scored with 50 during Australia's meagre innings but left the field after the 19th over of Sri Lanka's run chase.
The Lankan batsmen were never troubled with Thirimanne, making his maiden one-day international ton, and experienced opener Tillakaratne Dilshan (57) timing the chase like precision clockwork.
The pair were united after just three balls when Clint McKay dismissed Upul Tharanga for a duck, and responded in style with a match-defining 137-run partnership for the second wicket.
First-gamer Cutting (1-42) ended the union by dismissing Dilshan, after the Queenslander earlier made a handy contribution with the bat.
Cutting partnered Haddin in a 57-run stand after the Australians crashed to 6-83, with four of the top six batsmen failing to reach double figures.
Only David Hussey (29) and stand-in skipper George Bailey (26) contributed amid a middle order collapse of 4-32 which cruelled any Australian hopes of posting a competitive total.
Aaron Finch (four) failed again, Phil Hughes made three, Glenn Maxwell eight and Steve Smith, who surprisingly replaced Usman Khawaja, also managed just eight.
Sri Lankan quick Lasith Malinga claimed 3-32 as the Australians were bowled out in the 47th over.
Australian coach Mickey Arthur said regular captain Michael Clarke, Wade and David Warner would now all return from their enforced rests.
Arthur said Johnson and Starc would also be available for selection for Friday's third game in Brisbane, while the extent of Haddin's hamstring strain would be determined on Monday.
Sri Lanka's man of the match Thirimanne said the tourists were proud of the way they responded from their Melbourne loss, and were ignoring debate about whether they were playing Australia's 'B team'.
"We won't think about it that way, if it's Australia A or Australia B, it doesn't matter, we just want to win the series," he said.
- AAP
