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.
In other matches on the day, Sri Lanka coasted to a convincing seven-wicket win over Ireland in Group D with opener Dhananjaya Lakshan slamming a fine unbeaten 101 from 120 deliveries with the help of eight fours and a six.
However, Lakshan's unbroken 157-run partnership with captain Kamindu Mendis, who remained unbeaten on 74, took the team through.
Earlier, Mendis had also grabbed 3/35 with his spin bowling to restrict Ireland to 206/8 in the 48-over match after openers Jamie Grassi (75) and Mark Donegan (36) had provided the Irish a 73-run opening stand.
In Group A, South Africa piled on a massive 341/7 after electing to bat first.
He was involved in a 125-run second-wicket stand with left-handed opener Jiveshan as the Proteas virtually batted the opposition out of the contest.
Pillay scored 62 runs off 67 balls with seven fours and a six.
Kenya were never in the chase and eventually finished at 172/7 in 50 overs. They had been reduced to 50/4 in the 19th over and then 98/6 in the 34th.
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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