Australia now lead the four-match series 1-0.
Chasing a target of 364, India were bowled out for 315 in 87.1 overs despite skipper Viart Kohli's brilliant knock of 141 and his partnership of 182 for the third wicket with Murali Vijay (99).
Off-spinner Nathan Lyon grabbed 7/152 and his match-haul of 12 wickets set up the victory for the home team.
Brief Scores: Australia 517/7 decl & 290/5 decl
India 444 & (target 364) 315 in 87.1 overs (Virat Kohli 141, M Vijay 99, Nathan Lyon 7/152). Australia won by 48 runs.