The India captain's dashing innings -- he faced just 41 balls, including seven fours and eight sixes -- was the cornerstone of a total of 205-5 made after Australia skipper Mitchell Marsh won the toss in this Super Eights match.
India star batsman Virat Kohli holed out for a five-ball duck off Josh Hazlewood, who took an impressive 1-14 in his maximum four overs, with Tim David taking a fine running catch over his shoulder.
But fellow opener Rohit then cut loose. He was particularly severe on Mitchell Starc, the only change to the Australia team that suffered a shock 21-run defeat by Afghanistan last time out.
He hit the left-arm fast bowler for 29 runs in a third over where he struck four sixes -- two in successive balls over extra-cover, a monster hit over deep midwicket and a top-edged full toss over the wicketkeeper.
But with Rohit threatening to the first hundred of this tournament, Starc bowled him with an excellent yorker to leave India 127-3 in the 12th over.
Although the run-rate slowed, Suryakumar Yadav (31), Shivam Dube (28) and Hardik Pandya (27 not out) all made useful contributions.
"It was like a dream watching Rohit, he batted so beautifully," said Suryakumar Yadav during the innings break. "Before coming here, we spoke about how we wanted to go about things with the bat and he showed us the way.
"It's a good score but it is a good pitch. There is something for the bowlers, so hopefully we can use that and defend the total."
Starc did well to finish with 2-45 as fellow paceman Pat Cummins went wicketless while conceding 48 runs.
Victory for India, beaten on home soil by Australia in the final of last year's 50-over World Cup, would put them into the semi-finals.
An Australia win will likely see them into the last four but they will not necessarily be eliminated if they lose, with Afghanistan in action against Bangladesh later Monday.
