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Calm centurion Usman Khawaja, crafty legspinner Adam Zampa and clinical paceman Pat Cummins enhanced their reputations as Australia won the series decider in Delhi by 35 runs.
Khawaja scored 100 in a total of 9-272.
India crashed to 6-132 in response and were bowled out for 237, marking the first time Australia have battled back from 0-2 down to win a five-match bilateral ODI series.
The three confidence-building victories came after Australia had won just four of their past 26 completed one-dayers.
"People have written us off for quite a while," captain Aaron Finch said.
"We always knew that the plans and the style that we wanted to play are all there, can win us the World Cup, win us big series against great teams.
"The resilience and fight that we showed - being down 2-0 it would have been easy to roll over ... we've had our backs against the walls for quite a while now, so I'm really proud of the group."
Coach Justin Langer also praised Australia's "unbelievable fight and great character", while India skipper Virat Kohli credited the opposition for showing more "passion, hunger and heart than us in the last three games".
"They were brave in the pressure situations compared to our side," Kohli said.
Australia banked their first ODI series win in India since 2009, first overseas ODI series win since 2016, first ODI series win since 2017 and plenty of momentum in their march towards the World Cup.
Kohli's star-studded outfit had been widely expected to be England's greatest threat at this year's World Cup but Australia's batsmen and bowlers have both stepped up on the current tour.
None more so than man of the series Khawaja.
The left-hander started the series turnaround with a maiden ODI ton in Ranchi and bettered Kohli to finish the leading run-scorer of the series, all but cementing his spot in the 15-man World Cup squad.
A collapse of 6-54 followed Khawaja's dismissal then Cummins and Jhye Richardson ensured the tail wagged, taking 42 runs off the final four overs.
A seventh-wicket stand of 91 runs between Kedar Jadhav and Bhuvneshwar Kumar created some nervous moments for the visitors but it was snapped when Cummins claimed his 14th wicket of the series.
Zampa hammered home Australia's advantage with three quick wickets in the space of 14 deliveries, while recalled offspinner Nathan Lyon was Australia's most economical bowler with 1-34.
Australia's selectors suddenly have the good sort of headaches, rather than scrambling to find batsmen capable of delivering match-winning innings in the absence of Steve Smith and David Warner.
Ashton Turner, who starred with 84 not out as Australia chased down a record 359 to win the preceding game, scored 20 on Wednesday after being preferred ahead of Shaun Marsh.
Australia travel to Dubai on Thursday for a five-match ODI series against Pakistan, which will be the final chance for players to impress before selectors name a 15-man World Cup squad.