Australia have secured the four-match series over India, but have not won the third Test in Melbourne after they failed to take their final four wickets on day five.
India reached 174-6 to draw the match, which marked the first time that a Test has been drawn at the MCG in 17 years.
India were given the chase of an unlikely target of 384 after the hosts declared on 318-9 in their second innings.
After snatching three wickets before tea, Australia struggled to break the partnership of Virat Kohli and Ajinkya Rahane, but the breakthrough eventually came when Ryan Harris dismissed Kohli for 54.
Cheteshwar Pujara (21) followed 37 runs later when he was bowled out clean by Mitchell Johnson, who claimed his second wicket of the innings.
It looked as though India, who lost eight wickets in the final session in their Adelaide Test, were on the verge of collapsing once again as Josh Hazlewood took the wicket of Rahane (48), who top-edged a pull to midwicket.
It was a tense finish as Australia needed four wickets in 12 overs to win the Test, but MS Dhoni and Ravichandran Ashwin held firm as they closed the Test unbeaten on 24 and eight runs respectively.
