Chasing 393 for victory, Sri Lanka were bowled out for 255 in the last hour of play on the final day. Kumar Sangakkara was the topscorer with 63 while Thilan Samaraweera made 49.
Siddle took four wickets in the second innings and finished the game with nine scalps. He was named Man-of-the-match.
Starc took five wickets in the second innings including the last batsman in the 120th over.
Australia lead the three-match 1-0. Second Test begins in Melbourne on December 26.