Batting first, Australia guided by Shane Watson's ton and Tim Paine's fighting 92 scored 428.
In reply, India scored 405, with Tendulkar and Raina scoring 98 and 86 respectively. Mitchell Johnson starred with the ball, ending with figures of 5/64.
Australia had a crucial 23 run lead, but could only manage 192 in their second innings, setting India a target of 216.
India were struggling at 124/8 and it seemed Ricky Ponting would finally get his elusive victory on Indian soil, but then Ishant Sharma and VVS Laxman came together to stitch a 81-run partnership.
Ishant faced 92-balls for his 31-runs and had answers to everything that the Aussies threw at him
But there seemed to be another twist in the tale, as he was dismissed with 11 runs still required.
Laxman was battling a major back problem and using a runner, at one point there was all sorts of confusion, with Laxman shouting his lung out at Pragyan Ojha.
But in the end, it was Ojha who scored the winning runs, as India completed another memorable victory over the Aussies.
First Published: October 5, 2017, 4:10 PM IST