Scorecard
It was the fifth occasion when Sharma and Dhawan got engaged in a 100-run partnership.
Sharma's 79 run knock was studded with three sixes and seven boundaries. Both openers had kept Australia after they posted an imposing 350/6.
Earlier, Shane Watson and George Bailey hit century each to power Australia to a big total.
Big and burly Watson struck 13 fours and three sixes in making 102 off 94 balls while the in-form Bailey was equally impressive in scoring a career-best 156, his second ODI ton, in 115 balls. His brilliant innings contained half a dozen sixes and 13 fours.
These two batsmen also compiled the second-highest third wicket stand of 168 in ODIs against India to help the visitors record their fourth 300-plus total in the series in which the sixth ODI at Cuttack was totally washed out.
The home team, which needs to win this game to stay alive in the series in which they trail 1-2, started off well by sending back openers Phil Hughes (13) and Aaron Finch (20) before the score had crossed 50 but were pushed into the backseat as Watson and Bailey launched a superb counter-attack.
The duo simply tore apart the clueless Indian bowling attack that fielded three frontline spinners for the first time in the seven-match series after the hosts decided to go in with Amit Mishra to partner R Ashwin and Ravindra Jadeja.
Later, after the dismissal of Watson and Glen Maxwell (9), Adam Voges (44 not out) helped his captain add another 120 runs in only 80 balls for the fifth wicket to complete India's misery on a good batting track.
While the 32-year-old Watson was all power, Bailey, who has been the team's most consistent batsman in the series, once again dominated the home team attack to notch up his fourth 50-plus score in five innings.
India had the visitors under check in the first 20 overs by restricting Australia to 83/2 but the middle overs were totally dominated by Watson and Bailey who compiled the second-best-ever third wicket stand for their country against the hosts.
The 168-run partnership, that came off just 142 balls, was only the second-highest after Ricky Ponting and Damien Martyn's unfinished 234 in the 2003 World Cup final at Johannesburg and the eighth 150-plus stand for all wickets against India.
Watson, who compiled his maiden hundred against India and ninth in ODIs overall from 170 games, looked assured in his footwork against the trio of home team spinners, who bowled the middle overs.
Bailey was as solid as he has been in the series so far and showed his supreme touch quite early by hitting Mohd Shami for three successive boundaries in the bowler's opening spell.
India, who started well after Mahendra Singh Dhoni had asked the visitors to take first strike on winning the toss, were pushed on the backfoot by the aggression shown by this duo of batsmen.
All the bowlers were punished mercilessly with Ashwin emerging as the most successful with a haul of two for 64 in his 10-over quota along with Jadeja, who took two wickets in the innings' last over after conceding 68 runs.
Mishra, who was treated with absolute disdain after a watchful start by Watson and Bailey, conceded 78 runs respectively. Jadeja grabbed two wickets in his and the innings' last over.
Mohd Shami, who made an impressive beginning when he was given a chance in the rained-out Ranchi ODI, was very expensive and finished with 1 for 66 while Bhuvaneshwar Kumar, back in the squad after missing out the Ranchi ODI, had final figures of one for 42, the most economical among all bowlers.
Watson was lucky to have been caught off a no-ball from Jadeja as he mistimed a heave to leg but otherwise looked totally in control and in terrific form.
He was harsh on the three spinners and lofted Mishra who began impressively before being carted around for two leg side sixes out of the three he hit along with 13 fours in his punitive innings.
Watson reached his hundred in great style by hitting the expensive Shami for three successive fours before the bowler got his revenge off the fourth by clean bowling him through the gate.
Australia lost Glen Maxwell immediately afterwards when Ashwin, who was again guilty of bowling a number of hittable balls, had him caught just inside the boundary line by Bhuvaneshwar Kumar for his second wicket.
But none could stop Bailey from marching on to score the second hundred of his 34-match ODI career after missing out the landmark earlier in the series. Australia added 137 runs in the last 15 overs, including 54 in the last five.