Bailey emphatically underlined his Ashes credentials with a spectacular 156 off 114 balls, while Watson hit 102 off 94 balls in Australia's total of six for 350.
Bailey's was the ninth-biggest ODI score by an Australia and the highest individual knock at the VCA stadium.
He is the form batsman in the series, compiling 474 runs at an average of 118.5 - though Kohli's 344 at 172 is also highly impressive.
Bailey's odds of lining up for the Gabba Test are shortening with every innings.
The only thing missing from his achievements this tour was reaching three figures, a mark he reached off 84 balls on Wednesday.
His 168-run partnership with Watson lifted Australia from a dire position after openers Phil Hughes (13) and Aaron Finch (20) both went cheaply.
But his magnificent knock was the furthest thing from his mind as India reprised the sort of form that broke all the records in Jaipur.
As in Jaipur, India's remarkable chase was set out by a monster opening partnership of 178 to Rohit Sharma and Shikhar Dhawan.
And just like in Jaipur, Kohli blasted a blistering century - this time off just 61 deliveries - to thrust India towards victory.
Also, like in Jaipur, Dhawan was dropped early in his innings and went on to make the Australians pay - posting an even 100 for his fourth ODI century.
In Nagpur, Glenn Maxwell put down a relatively simple chance by his standards with Dhawan on 18.
The erratic left-hander went on to spearhead the chase with an aggressive 102-ball innings.
Dhawan was well supported by the stroke-playing Rohit Sharma, who finished with 79 from 88 before he was well caught in the deep by James Faulkner off part-time spinner Aaron Finch (1-20).
As you would expect with a score like this, no Australian bowler was spared.
Mitchell Johnson picked up wickets of Suresh Raina (15) and Yuvraj Singh (0) but conceded 72 runs from his ten overs.
Shane Watson had 0-50 from six, Clint McKay's seven overs cost 47 runs and Finch was the only bowler with an economy rate of five or less.
Needing 20 from the final two overs, India took 14 from Watson's sixth over to leave the equation at just six from the final over.
On a day when over 700 runs were scored, it was never likely to be an insurmountable task - and it wasn't, as MS Dhoni (25no) hit the winning runs.
