Opener Usman Khawaja hit his second hundred in three matches to guide Australia to 272-9 from their 50 overs.
The hosts were bowled out for 237 as Australia claimed victory.
"It is a very god result, given how tough a summer it has been". "The resilience and the fight that we showed was incredible ..." It was India's first series loss at home since October 2015 and Australia's first ODI series win in India in a decade.
Australian cricket has suffered a torrid year since Smith, Warner and Cameron Bancroft were banned for ball-tampering during a Test last March, an incident that prompted a national outcry.
Kohli suggested the tourists were hungrier in the final three ODIs of the series, likening their approach to that which India adopted in Australia.
"Man of the series in a one-day tournament in India, I wasn't even in the one-day side this time past year", he told reporters after the match.
- Kuldeep Yadav conceded 74 runs while taking a wicket in the final ODI played at Feroz Shah Kotla Ground which is now his second-most expensive bowling figures in ODIs.
- This was the fifth instance of a team winning an ODI series after being 0-2 down.
Shankar has come a long way since his disastrous debut in the Nidahas T20 tri-series and could be a solid all-round option going forward for India if he continues to develop.
Coach Justin Langer said he was "incredibly proud" of a team who also swept the two-match Twenty20 series.
Australian players celebrate the dismissal of India's Rohit Sharma during the final one day global cricket match between India and Australia in New Delhi, India, Wednesday, March 13.
They slipped from 175-1 to 182-4, before Jhye Richardson and Cummins helped them to a score of 279. "He wanted to know where he was at with white-ball cricket", Langer recalled after Khawaja's match-winning century in the Delhi decider.
The likes of Glenn Maxwell, Stoinis and Ashton Turner all failed to deliver significant innings with the bat, but it mattered little as the bowlers turned on the style to seal Australia's first series win in India since 2009. "Eventually, everyone will know no one wants to miss the bus to the World Cup and cost the team good balance".
A clearer picture will emerge after the ODI series against Pakistan in United Arab Emirates later this month, but the manner of their victory against India makes Finch confident of their title defence at the World Cup.