The visitors started well in the first half before the Indian bowlers struck twice. Ravichandran Ashwin got the first wicket while Shami scalped the second.
Chasing a modest target of 243 runs, India crossed the line with 43 balls still to go.
India restricted Australia to 242 runs for nine wickets in 50 overs.
Former Australian pacer Rodney Hogg has accused Steve Smith of favouritism in team selection.
Dravid feels Pandya is a perfect example of how to bat differently in different conditions.
India opener Ajinkya Rahane on Saturday praised spin pair Yuzvendra Chahal and Kuldeep Yadav.
It was no small task for Virat Kohli and his men to defend a modest 252 on the Eden Garden wicket, which despite being a two-paced track favoured the batsmen.
