Australia had looked well set to take a 2-0 lead in the seven-match series after compiling 359 for five batting first at Jaipur, with all of their top five contributing half-centuries and captain George Bailey leading the way with a brilliant unbeaten 92.
However, those knocks were all overshadowed by India's top three as Sharma (141 not out), Kohli (100 not out) and Dhawan (95) put Australia's bowling attack to the sword in brutal fashion as the host nation romped home with over six overs to spare.
Kohli's 52-ball knock, which included seven sixes and eight fours, was the fastest ODI century by an Indian and seventh fastest ever, while Sharma was similarly destructive as he clubbed 17 fours and four maximums in his 123-ball innings.
Dhawan was no slouch either as he collected 14 boundaries before falling just short of his ton when he edged the 86th ball he faced, bowled by James Faulkner, behind to Brad Haddin, who had earlier dropped the opener off a steepling leading edge when he was on 18,
That wicket brought an end to an opening stand of 176 in 26 overs but was the only success Australia's bowlers enjoyed on what was undoubtedly a batsman's day.
Earlier, it was the India attack who found themselves on the receiving end of some brutal batting as Australia, who won the first ODI by 72 runs after running up 304, set what had appeared to be a tough target.
Skipper Bailey led the from the front with 92 off just 50 balls, including five sixes and eight fours, while Phil Hughes (83), Shane Watson (59), Glenn Maxwell (53) and Aaron Finch (50) were also amongst the runs.
However, that total proved to be nowhere big enough as India chased it down in style.
It was the second-highest successful run chase in ODI history, with only South Africa's famous one-wicket win over Australia in 2006 when the Proteas reached a target of 435 topping it.
When faced by such a large target on Wednesday, India captain Mahendra Singh Dhoni told his batsmen to go out and express themselves and also reminded them of a match against Sri Lanka four years ago which almost produced another amazing run chase.
On that occasion, India made 414 for seven batting first and Sri Lanka fell agonisingly short on 411 for eight.
Dhoni said on Sky Sports: "Irrespective of the rule changes and how good the track was, I still think 350 odd runs is still not an easy task to chase.
"In the break I just told them that we played a game once before when we scored 414 runs and Sri Lanka managed to get close. I said just go out there, don't look at the target, be expressive on the field and just don't lose your shape when you're going for your big hits."
Defeated Australia skipper Bailey, meanwhile, described India's onslaught as "awesome".
"I'm not sure what to feel at the moment, that was some pretty awesome batting. Obviously there's things you do differently with the ball, but I think to be fair and to be reasonable to India, it was just awesome batting," he said.