The stalemate in Melbourne means Australia, thumped 4-0 when the teams last met in Test cricket in 2013, are 2-0 up with one to play in the four-match series , having won the first two Tests in Adelaide and Brisbane.
Steven Smith???s side tried to force victory at The MCG on Tuesday when they put India into bat after lunch but despite taking three early wickets and latterly dislodging Virat Kohli, the Baggy Greens were left frustrated as the tourists battled to 174-6 before Smith conceded the draw with four overs remaining.
Opener David Warner declared on the evening of day four that Australia needed more than the 326-run lead they had accrued over India before pushing for a win and Shaun Marsh duly obliged in the morning session.
The 31-year-old moved on from his overnight 62 to 99, with the highlight of his knock when he clobbered Ravichandran Ashwin for a six and a four off successive balls to reach 96.
Marsh missed out on his third Test century when he was run out by Kohli ??? the 16th player in Test history to depart in that fashion on 99 ??? but he and Ryan Harris (21) ensured Australia were able to call time on their innings at 318-9 at lunch.
India, therefore, were set an MCG record 384 runs from 70 overs to win the third Test and keep themselves in the series, though the visitors were surely more concerned with salvaging a draw.
MS Dhoni???s charges began their second innings in the worst possible way when they lost Shikhar Dhawan (0), Lokesh Rahul (1) and Murali Vijay (11) within the first nine overs to sink to 19-3.
Dhawan was dismissed lbw by Harris; Rahul, surprisingly promoted to No 3, edged Mitchell Johnson to the slips; and Vijay was then victim of a harsh lbw decision, with replays showing the ball clattered into his pads by Josh Hazlewood was missing leg stump.
However, Kohli (54) and Ajinkya Rahane (48) ??? who combined to put on a fourth-wicket stand of 262 during India???s opening knock in Melbourne ??? added 85 before Kohli lofted to Joe Burns at square leg.
Kohli???s exit made India a bit jittery and they were even more flustered when Johnson flattened the off stump of Cheteshwar Pujara (25) and Rahane miscued a pull stroke off Hazlewood and was plucked by Marsh, but, at 142-6, Dhoni (24 not out) and Ashwin (8 not out) dug in to survive a tense final hour.