The victory enabled the hosts clinch the seven-match series 3-2.
The 26-year-old Sharma came up with a breathtaking display to power India to an imposing 383 for 6 before they dismissed Australia for 326 in 45.1 overs at the jam-packed Chinnaswamy stadium.
The immensely talented Sharma thus became only the third batsman in the history of ODIs, after Virender Sehwag (219) and Sachin Tendulkar (200 not out), to register the coveted double hundred.
Chasing a mammoth total, Australia made a spirited effort, with all-rounder James Faulkner blasting a 73-ball 116, the fastest century by an Australian in ODIs.
While he hit 11 fours and six over-boundaries, Glenn Maxwell pulverized the Indian bowlers on his way to a 22-ball 60 that was studded with seven sixes, which was not enough in the end.
Staring at a heavy defeat at 138 for six, Faulkner played a blinder as Australia made a dramatic recovery to give their chase respectability. He was involved in a record ninth wicket stand of 115 runs with Clint McKay.
Earlier, en route his 158-ball-209, Rohit created a world record by hitting as many as 16 sixes and 12 fours. His effort bettered Shane Watson's previous best of 15 maximums against Bangladesh.
Skipper Mahendra Singh Dhoni (62) and Shikhar Dhawan (60) scored brisk half-centuries to boost India’s total.
This was also the highest individual ODI score by any batsman against Australia in ODIs, as well as India's highest team total against the visitors.
The last five overs produced an unbelievable 101 runs.
This is the first instance when India won a seven-match ODI series against the Aussies.
While Rohit scored his first 100 off 114 balls, the next hundred came off only 42 deliveries. All the sixes were clean, straight hits in the arc between deep extra-cover and deep mid-wicket. There was minimum muscle and maximum timing in each and every six that he hit.
Put in to bat by Australia skipper George Bailey, the home team rode on Rohit's brilliant batting display, which was complemented by his opening partner Dhawan (60) and Dhoni, who batted in his customary style, smacking a 38-ball-62, inclusive of seven fours and two sixes.
Rohit and Dhoni added a staggering 167 runs for the fifth wicket in only 15.4 overs, at an average of 10.65, while the opening partnership again proved productive, yielding 112 runs.
The men who missed out included Virat Kohli (0)and the two horribly out-of-form players Yuvraj Singh (12) and Suresh Raina (28).
While another in-form batsman Kohli was run-out for a duck, without scoring, and looked angry, the Delhi star was the most vocal in his applause when Rohit reached his individual milestones.
Having got second wind after being promoted as an opener, Rohit also completed 1000 runs in ODIs this year at a very impressive average of 50 plus.
This is Rohit's third big score in the current apart from his match-winning 141 at Jaipur and 79 in the last game at Nagpur.
The current ODI rules of having five fielders inside the circle at any point of time has proved draconian for bowlers.
All the frontline Australian bowlers got a hammering, with Clint McKay (1-89 in 10 overs) ending up with worst figures.
Nathan Coultier-Nile (0-80 in 10 overs), James Faulkner (1-75 in 10 overs) and Xavier Doherty (2-74 in 10 overs) were smoked to all parts of the ground by Rohit and Dhoni.
Rohit ultimately fell to Mckay when he was caught by substitute Moises Henriques, who had come in to field for Shane Watson, who suffered an hamstring injury.
Rohit and Dhawan brought up the third century opening stand for India in the series after he rocked back and cut Glenn Maxwell to deep extra cover fence. This was also their sixth century stand this year and they became the only pair to do so in a calendar year.
They were also involved in match-winning 176 and 178 runs opening partnerships in the Jaipur and Nagpur one-dayers respectively.
Dhawan was lucky to survive on 41, when Watson missed a run-out chance at backward point after he threw the ball wide, giving ample time for the Delhi lad to get back into the crease.
Doherty did the damage for the visitors, scalping two important wickets of Dhawan and Suresh Raina, and pegged India back to some extent after the roaring start given by the openers.
Kohli, who needed 81 runs to beat Vivian Richards's record of being the fastest batsman to reach the 5000-run mark in one-dayers, was unfortunately run-out.
Raina and Yuvaraj fell to Doherty and James Faulkner in quick succession but Rohit and Dhoni more than made up for their failures.
While batting, Australia lost six wickets with just 138 runs on the board before the lower-order, led by the mercurial Faulkner, staged a recovery.
In a match that saw quite a few records tumble one after another, medium pacer R Vinay Kumar was the only bowler to bleed more than 100 runs.
When Faulkner walked out to bat, Australia were reeling at 132 for five, but, in a matter of few overs, he nearly changed the equation by striking a barrage of fours and sixes.
But with the visiting side losing their top-batsmen with little on the board, even the heroics of Faulkner and Co could not help Australia chase down the target.
Mohammed Shami, Ravichandra Ashwin and Ravindra Jadeja finshed with two wickets apiece.
Image: Rohit Sharma
Photograph: BCCI
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