Rahane, deputising throughout Virat Kohli’s paternity depart, hit an unbeaten 27 in Melbourne — after a century within the first innings — as India reached the meagre goal of 70 for the lack of two wickets.
It capped a outstanding comeback for an Indian crew determined to make amends after dropping in Adelaide by eight wickets, once they posted their lowest ever rating of 36 and have been broadly criticised at house.
They usually bounced again with out famous person and batting maintstay Kohli, who has returned house for the start of his first youngster.
Beneath the mild-mannered Rahane, they battled laborious to dismiss Australia for 195 within the first innings after which posted 326 in reply.
Australia resumed their second innings on day 4 on 133 for six with a two-run lead, and their hopes resting on 21-year-old rookie all-rounder Cameron Inexperienced.
He made 45 as they battled to 200 earlier than tail-ender Josh Hazlewood was the final man to fall earlier than lunch.
Mohammed Siraj, on debut, took 3-37 with Jasprit Bumrah, Ravindra Jadeja and Ravi Ashwin grabbing two every.
Rahane and one other spectacular debutant, Shubman Gill (35) then noticed India house, however not earlier than some nervous moments.
Mitchell Starc obtained a nick from the out-of-form Mayank Agarwal (5), which Tim Paine caught, then Pat Cummins snared Cheteshwar Pujara for 3, edged to Inexperienced at gully.
It left India on 19 for 2 earlier than they regained their composure to seal the win.
Australia collapsed to 99 for six within the run chase on Monday earlier than Inexperienced and Cummins knuckled right down to climate 18 overs and steer them to stumps.
Inexperienced, who has been on hearth with the bat within the home Sheffield Defend this season, confirmed glimpses of his magic, chopping Ashwin and driving Bumrah superbly for fours, whereas additionally exhibiting persistence.
However Inexperienced, in solely his second Check, was undone by Siraj, caught by Jadeja as he appeared to seek out the boundary with a pull shot, ending a 146-ball keep.
Cummins survived possibilities on 15 and 19, however when Bumrah took the brand new ball and located extra swing and bounce he lastly fell, gloving a rising supply to Agarwal to finish a battling 57-run partnership with Inexperienced.
Starc was unbeaten on 14 with Nathan Lyon caught behind off Siraj for 3, and Hazlewood making 10.
Australia’s hopes rested with the tail-enders after their prime order failed to fireplace, exposing the delicate nature of their batting within the absence of the injured David Warner.
Opener Joe Burns once more flopped, out for 4, to place his place within the crew for the third Check subsequent week at severe threat, whereas Travis Head (17) additionally disenchanted and Steve Smith’s poor run continued, gone for eight.
Their troubles got here regardless of India being a bowler down following Umesh Yadav’s calf pressure on Monday, an additional setback for a crew already lacking injured regulars Mohammed Shami and Ishant Sharma.
Regardless of this, India’s assault rose to the event, with Bumrah on the prime of his recreation and younger paceman Siraj impressing, whereas skilled spinners Jadeja and Ashwin constantly posed issues.
Bumrah took 4-46 in Australia’s first innings and Ashwin 3-35, nevertheless it was Rahane’s gritty 112 that in the end proved match-winning.
He got here to the crease along with his crew in bother at 64 for 3 and, towards one of many world’s most potent bowling assaults, reached a 12th Check century, one which pundits rated as maybe his most essential ever.
The third Check is because of begin on January 7 in Sydney.