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Chasing a mere 70 to win, India overhauled to target in 15.5 overs with more than four sessions to spare.
India had lost the pink-ball Test in Adelaide.
Skipper Ajinkya Rahane (27 not out) and opener Shubhman Gill (35 not out) took the side past the finish line after India lost Mayank Agarwal (5) and Cheteshwar Pujara (3).
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India had taken a 131-run lead on the third day with skipper Ajinkya Rahane (112) and Ravindra Jadeja (57) taking the hosts to 326 in reply to Australia”s first innings total of 195.
Number six Cameron Green was top-scorer for the hosts with his 45-run knock while make-shift opener Matthew Wade made 40.
Green and Pat Cummins (22) added 57 runs for the seventh wicket with the pitch offering nothing to the bowlers. The partnership was broken only after the new ball was taken.
For India, debutant pacer Mohammed Siraj (3/37) took three wickets while Jasprit Bumrah (2/54) and Ravindra Jadeja (2/28) and Ravichandran Ashwin (2/71) took two wickets apiece.
Brief Scores:
Australia: 195 and 200 in 103.1 overs (C Green 45, M Wade 40, M Labuschagne 28; M Siraj 3/37, R Jadeja 2/28, J Bumrah 2/54)
India: 326 and 70 for 2 in 15.5 overs. (S Gill 35 not out, A Rahane 27 not out; M Starc 1/20, P Cummins 1/22).