Chasing 288 to win, Rohit scored 133 off 129 balls but it was a top-order collapse and a failure to keep up with the run-rate in the middle overs which handed the home team the win and a series lead.
Jhye Richardson was the pick of the bowlers for Australia, returning figures of 4-26 in his 10 overs. He was ably supported by Jason Behrendorff and Marcus Stoinis, who took two wickets apiece.
Australia's innings was a case of multiple small partnerships leading to a late flourish. Opting to bat, they lost skipper Aaron Finch early when Bhuvneshwar Kumar got through the defence with an inswinger.
Alex Carey impressed for a while before he nicked to Rohit Sharma at slip in Kuldeep Yadav's first over, leaving Australia 41 for 2 in the tenth over.
The stable partnership came from Usman Khawaja and Shaun Marsh, both left-handers getting half-centuries. They took their time, scored in singles and doubles but set the base in the middle overs. Khaleel Ahmed was expensive, which forced India to even make Ambati Rayudu bowl a couple of overs.
Khawaja fell in the 29th over, trapped leg before trying to sweep Ravindra Jadeja. Marsh carried on, with a busy Peter Handscomb taking care of the scoring, before he fell trying to attack Kuldeep.
It was the 38th over then but there was no sign of Glenn Maxwell. Instead, it was Marcus Stoinis who came in. Stoinis took time to settle down, Australia lost a bit of momentum and there was no boundary between over 35.5 and 43.3.
That changed when Stoinis and Handscomb took the attack to Kuldeep, beginning Australia's charge. Handscomb unleashed his cheeky self, before falling to Bhuvneshwar Kumar while going for a second six in the 48th over.
Bhuvneshwar was expensive in the death, his last over going for 18. He ended with 2 for 66 from his 10 overs, while Kuldeep got 2 for 54. Australia managed 93 runs in the last 10.
India had a nightmare start to their chase, with two rookie pacers running through the top order, leaving them 4 for 3. Shikhar Dhawan was trapped leg before for a first-ball duck by Jason Behrendorff. Richardson then bagged Virat Kohli and Ambati Rayudu in the fourth over; Kohli flicking to square leg and Rayudu was trapped lbw by one that nipped in.
To make things worse, Rayudu also used up the review, which would hurt Dhoni later on.
What followed was a phase where both Rohit and Dhoni, especially the latter, went into a shell. The first goal then was to arrest a collapse.
The duo did that successfully, although India managed only 21 runs in the first 10 overs. Dhoni was on 6 off 7 runs at one stage. Rohit wasn't much quicker either, his first 35 balls yielding only 12 runs.
But the duo also picked their bowlers to start shifting gears. Dhoni launched a big six off Nathan Lyon, while Rohit got going hooking Peter Siddle for a six. The first four of the innings came only in the 21st over.
Rohit stepped foot on the pedal, moving to his half-century off 62 balls. Dhoni, meanwhile, got a reprieve when Siddle dropped a tough chance at short mid-wicket. He was struggling with a leg niggle, but battled on with quick running and the occasional four, one of which gave him his half-century off 93 balls.
Three balls later, he was given lbw to Behrendorff with the ball pitching outside leg, but he didn't have a review.
India needed 148 to win off 106 at that stage, and the only hope was Rohit staying till the end. Dinesh Karthik hung around for a while but fell to a cross-batted shot for 12.
Rohit battled on, getting to a brilliant century, keeping India alive but when he holed out to Maxwell off Stoinis’ bowling, any slim hopes the visitors had of winning the match evaporated.
Peter Siddle then accounted for Kuldeep Yadav whereas Stoinis dismissed Shami on the final ball on the innings.
The second ODI takes place at Adelaide on Tuesday (January 15).
Aaron Finchambati rayuduGlenn MaxwellIndia vs Australia 2018India vs Australia first ODI in SydneyJason BehrendorffJhye RichardsonKuldeep YadavMS Dhonirohit sharma
First Published: January 12, 2019, 4:03 PM IST