Rampaging Rohit leads India into T20 World Cup semis with Australia on brink of elimination
Rohit clobbered eight sixes in his 41-ball blitz to lay the foundation for India's imposing 205-5, their highest total in the tournament, in Gros Islet, St Lucia.
Travis Head led Australia's chase with a belligerent 76 but India managed to restrict them to 181-7 to remain unbeaten in the tournament.
The Super Eight clash between two former champion teams had assumed greater importance after Afghanistan stunned Australia on Saturday to throw Group 1 wide open.
Josh Hazlewood drew first blood as he bounced out Virat Kohli for a duck after Australia elected to field.
Rohit has not been in the best of form but the India captain threw Starc out of the attack by hitting the fast bowler for four sixes in a 29-run over.
Pat Cummins, who claimed back-to-back hat-tricks in his last two games, was pressed into service to end the batting carnage.
Rohit greeted him by depositing the seamer's first ball on the roof of the stadium for a monster six en route to a 19-ball fifty, his first of the tournament.
India raced to the 100-mark in the ninth over but Starc returned to deny Rohit what could have been the first hundred by a batter in this tournament.
Suryakumar Yadav (31) and Shivam Dube (28) produced breezy cameos and Hardik Pandya made 27 not out to propel India to their first 200-plus total of the tournament.
Arshdeep Singh rattled Australia by removing David Warner in the first over in what could be the opener's last game in an Australia shirt.
Mitchell Marsh (37) joined Head and they counter-attacked to put Australia's chase back on track.
Axar Patel leapt to take a stunning one-handed catch at deep square leg to dismiss Marsh but Head raced to a 24-ball fifty.
Kuldeep Yadav castled the dangerous Glenn Maxwell (20) and Jasprit Bumrah effectively sealed India's victory when he dismissed Head with a clever change of pace.