Chasing 310 to win, Australia managed to reach the target in 49.2 overs.
Captain Steve Smith missed out on his 150 by one run as he was dismissed on 149 runs. His knock included 11 fours and two sixes.
Bailey also scored 112 runs for his side from 137 balls which included seven boundaries and two sixes.
India, choosing to take guard, scored 309 runs in their 50 overs.
Rohit Sharma scored an unbeaten knock of 171 runs from 205 balls which included 13 fours and seven sixes while Virat Kohli made 91 runs from 148 balls which included nine fours and a six.
Australian bowlers James Faulkner and Josh Hazlewood took two and one wicket respectively.
Indian left arm fast bowler Barinder Sran, making his ODI debut for the side, dismissed openers Aaron Finch and David Warner early before Smith and Bailey took control of the innings.
Ashwin managed to take two wickets for the visitors and dismissed Bailey and Maxwell.