Skipper MS Dhoni's decision to bring part-timer Rohit Sharma into the attack got the reward as he struck in his first over to dismiss Clarke.
The match has been reduced to 32 overs per side after rain spoiled more than two hours game.
The quota of bowlers were also reduced after the rain disruption as two can bowl 7 overs while 3 will get a chance to bowl 6 overs.
Australia were 35/2 in 11 overs when the play was stopped due to heavy rain at MCG.
Skipper Michael Clarke (5*) and Matthew Wade (21*) were at the crease when the rain disrupted the play.
Earlier after opting to bowl, India gave Australia early blows when Vinay Kumar dismissed David Warner and Ricky Ponting.
Vinay struck in his successive overs to remove Warner and Ponting cheaply and reduced Australia to 19/2 in 7.5 overs.
Ponting, who made a strong comeback in the Test series after long rough patch, went on the back foot to slap it through covers but failed to control his shot that went straight to Suresh Raina.
Warner attempted a big heave across the line on a full length delivery. The ball curled in, travelled through the gap between bat and pad and rattled the stumps. Warner contributed only six runs in his 14 balls stay at the crease.
Earlier, Indian skipper Mahendra Singh Dhoni won the toss and again decided to field against the hosts.
Indian opener Virender Sehwag has been rested from the match, while veteran Sachin Tendulkar has been included in the playing XI.
For Australia, wicketkeeper-batsman Matthew Wade and all-rounder Dan Christian will make their ODI debuts.
Their pace spearhead Brett Lee is out of the match and the tri-series, also featuring Sri Lanka, due to a broken foot.
Lee picked up the injury during the second Twenty20 international against India on Friday.
Finally a win under their belt in what has been a highly disappointing tour, India would aim to carry the Twenty20 momentum into the ODI series.
After a 0-4 thrashing in the Tests and a loss in the first T20 against Australia, India tasted victory in the second T20, winning by eight wickets on Friday.
Teams:
India: Gautam Gambhir, Sachin Tendulkar, Virat Kohli, Suresh Raina, Rohit Sharma, Mahendra Singh Dhoni (capt), Ravindra Jadeja, Ravichandran Ashwin, Rahul Sharma, Praveen Kumar and Vinay Kumar.
Australia: David Warner, Matthew Wade, Ricky Ponting, Michael Clarke (captain), Michael Hussey, David Hussey, Dan Christian, Ryan Harris, Mitch Starc, Xavier Doherty and Clint McKay.
