The India opener struck 10 fours and six sixes in a dazzling knock but his side fell 3 4 runs short.
India’s reply started badly once they slipped to 4-3, however, Rohit’s knock gave them some expectation of success.
He put on 137 for the fourth wicket using MS Dhoni (51), who became only the fifth Indian batsman to maneuver 10,000 one day international runs during the course of his innings.
The partnership was completed once Dhoni had been given out lbw off Jason Behrendorff decided that would have been chased by a review had India never used their just referral.
The touristswho won the Test series for the first time down under, were consistently behind the run-rate but reached the previous six overs requiring 76 to win.
However, both Ravindra Jadeja and Rohit fell in quick succession to end any hopes of a late push for success, Jhye Richardson carrying 4-26.
The 2nd match in the series is currently in Adelaide on Tuesday in 03:20 GMT. There will be live comment on BBC Radio 5 live sports extra and on the web (UK only).