Australia elected to bat first after winning the toss and appeared to be on course to top 300 for a third game running, as Khawaja cruised towards an elegant hundred - sharing in 76 and 99-run stands for the first and second wickets with Aaron Finch (27) and Peter Handscomb (52), who followed up his maiden ODI hundred in Saturday's fourth ODI with a further fifty. "Unbelievable, the resilience and fight we showed, being 0-2 down, it would've been easy to roll over, but the fight we showed makes it a great achievement", said Finch in the post-match presentation ceremony.
It is only the fifth instance that a team has won a series after being down 0-2.
Only Rohit Sharma (56) could score a half-century, which included two reprieves. "He is just 21 and represents India in all 3 formats".
The assuring presence of skipper Virat Kohli (20) did not last long as he too departed early, caught behind while attempting a cut off Marcus Stoinis.
Cummins proved a nightmare for India's openers during the series, regularly striking with the new ball.
Some late hitting from Bhuvneshwar Kumar, who struck 46 from 54 balls, could not get India over the line.
Australia claims historic one-day international series win in India
Rishabh Pant (16) folded under pressure, caught off Nathan Lyon.
Cummins grabbed 14 wickets at 15.71 in the five matches and would have earned man-of-the-series honours if not for the efforts of Usman Khawaja, who scored two centuries in the series.
It was a game that had everything - a stunning century, a freakish dismissal, an early collapse, a huge fightback, a flying bat and a thrilling finish - but in the end, Australia claimed a famous victory over India in India.
Ten fours and two maximums helped him get to three figures in 102 balls on this occasion, Khawaja leading from the front with quality shots on both sides of the wicket.
Ravindra Jadeja replaced Yuzvendra Chahal in the Indian playing eleven while K L Rahul made way for Mohammad Shami.
It turned out to be a forgettable day for chinaman Kuldeep Yadav, who bled 74 runs in his 10 overs, although he dismissed risky Ashton Turner (20) cheaply.
Against Regional Stability, Peace to Not List Masood Azhar as Global Terrorist
Several American think-tank members slammed China for its decision delaying the Azhar listing. But China said it needed more time to examine the request, asking for a hold.