Sri Lanka held their nerve to win the thrilling game after dismissing Australia for 229 with five balls left in reply to their total of 238.
They now face Australia in the best-of-three match finals, starting in Brisbane on Sunday, while India's disappointing tour of Australia is over and they will head home this weekend.
It was a gripping finish with Australia needing 10 runs off the final over bowled by Nuwan Kulasekara, but David Hussey was caught by Tillakaratne Dilshan at long off with five balls remaining ending their hopes of a last-gasp win.
Hussey scored 74 off 74 balls and finished the tournament as the leading runscorer of all the three teams with 412 at an average of 82.40.
Lasith Malinga finished with four for 49 as skipper Mahela Jayawardene used eight bowlers to defend his team's modest total.
Match scores: Sri Lanka 238 (50 overs); Australia 229 (49.1 overs)
