The left-handed Head (90) and Labuschagne (63 not out) snuffed out India's push for a victory on the final day with a stand of 139 after nightwatchman Matthew Kuhnemann fell early for six.
Head, capping a successful series after being left out of the first Test, missed out on his century after being bowled by Axar Patel.
Regular opener Usman Khawaja did not to bat due to "lower leg soreness" after getting hurt while fielding on day four.
The match belonged to India's Virat Kohli, who hit a masterful 186 on day four to end a Test century drought of 1,205 days since his previous ton in November 2019.
The marathon 364-ball knock blocked every chance of a potential defeat for the hosts after Australia posted 480 on a vastly different pitch from the previous three Tests.
Kohli, one of the best players of his generation, recorded his 28th Test century to power India to 571 all out on Sunday as India managed a lead of 91 after their first innings.
Kohli's partnership of 162 for the sixth wicket with Axar, who hit his third half-century of the series with an attacking 79, marked India's dominance on Sunday.
Opener Shubman Gill hit 128 to lead India's reply and make the most of his opportunity after being added to the team in place of struggling KL Rahul in the third Test.
Indian spinner Ravichandran Ashwin stood out with his six wickets in Australia's first innings in the run-filled match.
Opener Khawaja with a stubborn 180 and Cameron Green, who hit his maiden international century with 114, had handed Australia the early advantage.
Australia bounced back from their two opening losses to win the third match in Indore in just over two days on a viciously turning track to keep the series alive until the final match.
Steve Smith led Australia in the final two Tests after regular captain Pat Cummins returned home to be with his seriously ill mother. She died last week.