Kohli, Rahane put India in control after Australia post 326
Resuming the day on 277/6, Tim Paine and Pat Cummins frustrated the Indian bowlers, adding 33 runs to take the score past 300 before Cummins was cleaned up by an Umesh Yadav delivery that found the top of his off stump.
That triggered a collapse, and Ishant Sharma made short work of the tail. He dismissed Mitchell Starc and Josh Hazlewood off consecutive balls and Australia were bundled out for 326.
The session belonged to Australia, though, after Starc had Vijay dismissed for nought at the stroke of lunch to send India in at 6/1. Their post-lunch session didn't look promising either, as Hazlewood went through KL Rahul with a yorker and reduced India to 8/2.
That is when Kohli joined Cheteshwar Pujara in the middle. The duo rescued India in a fine display of gritty batting, adding 62 hard-earned runs in the remainder of the session.
Kohli displayed controlled aggression – he picked three boundaries off one Hazlewood over, with flicks through mid-wicket, drives down the ground – even as Pujara absorbed the pressure, playing out 103 balls for his 24.
Not long into the final session, however, Starc had Pujara flaying down leg and induced an edge. Paine pouched it, and India's match-winner in Adelaide was back in the dressing room.
Rahane came in and showed plenty of intent early on, taking on the short balls and playing his shots. There was an intense period in which Cummins and Starc barraged him with short balls, but Rahane gradually became more assured in his stroke-making, even sending an upper-cut through third man for his first boundary.
Kohli joined in, pushing one to cover to bring up India's 100, and Rahane then cut another short delivery from Starc for six. The two carried on and Kohli soon brought up his first half-century of the series, off 109 balls.
Paine rung in the changes, bringing Nathan Lyon and Hazlewood into the attack, and the move nearly had the desired effect when Rahane outside-edged one off Hazlewood. It fell just short of the slip fielders, though, and when Hazlewood tried another short delivery, Rahane rocked back and cut it to the fence.
The duo brought up their 50-stand in 17.4 overs, and as the session wore on and the bowlers tired, Kohli unleashed the drives, sending a couple beautifully through covers.
Rahane then brought up his own half-century, off 92 balls shortly before stumps, and India will begin the third morning hoping for more of the same.