Indian pacers Shivam Mavi and Kamlesh Nagarkoti then picked up three wickets each as the Australians were dismissed for 228 in 42.5 overs.
The Indian pace trio of Mavi, Nagarkot and Ishan Porel clocked over 145 km per hour during their spells.
An injury to Porel was the cause cause of concern for the Indians.
Edwards returned figures of 4/65 with his right-arm medium pace and was the only Australian who stood up to the Indian bowlers, posting a 90-ball 73 before being bowled by left-arm spinner Anukul Roy.
The Indians dominated proceedings from the moment skipper Shaw won the toss.
Shaw led from ther front, scoring 94 runs in a 100-ball innings which contained eight boundaries and a couple of sixes.
Shaw received a second reprieve, again off Sutherland's bowling, when he mistimed a pull only to be caught at deep backward square.
They put together an opening stand of 180 runs to gift a strong foundation to the Indian innings.
Shubman Gill then hammered home the advantage with 63 runs off 54 balls with six boundaries and a six.
Abhishek Sharma provided a late flourish to the Indian innings with an 8-ball 23.
Except for Edwards, the rest of the the Australian bowlers had a forgettable day although off-spinner Param Uppal was economical over his eight overs with figures of 1/35.
The former champions then lost wickets at regular intervals as the Indian bowlers started to dominate.
India: 328/7 in 50 overs (Shaw 94, Kajra 86, Gill 63; Edwards 4/65) vs Australia: 228 in 42.5 overs (Edwards 73; Savi 3/45 Nagrakoti 3/29).
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