By
Australia scored 171 for four and restricted India to 140 for six.
Man-of-the-match Matthew Wade topscored with 72 off 43 balls in Australia's innings and India did not recover after falling to 81 for six in the 14th over.
India captain M.S. Dhoni topscored for his side with an unbeaten 48 while Dan Christian and David Hussey took two wickets each.
The second match in the series takes place at the Melbourne Cricket Ground on Friday.