India took a 91-run first innings lead on Sunday to put themselves in an unbeatable position heading into the final day of the only test in the series that lasted the full five days.
Australia declared on 175-2, batting resolutely to frustrate India, who have held the trophy since 2016-17 and registered their 16th consecutive home series victory.
Head made 90 and forged a 139-run stand with Labuschagne, who made 63 not out, before players from both sides shook hands at the Narendra Modi Stadium.
India also confirmed their place in the World Test Championship final against Australia in June following Sri Lanka's two-wicket loss to New Zealand in Christchurch earlier in the day.
"It was fantastic right from the word go," India captain Rohit Sharma said of the series at the presentation ceremony.
"You saw how exciting it was. In all the test matches that we played, there was something in it for every one.
"After playing good cricket for 40-45 days, we stand here with the result, which we are quite happy with."
India’s hopes of a third victory in the series hinged on a batting collapse but the wicket at the Narendra Modi Stadium did not deteriorate as much as their spinners would have liked.
Australia had sent out Matt Kuhnemann to open the innings with Head on Sunday after Usman Khawaja hurt his knee while fielding.
Kuhnemann, who faced 35 balls for his six runs, was unlucky to be given lbw to a Ravichandran Ashwin delivery which, replays confirmed, would have missed the stumps.
Axar Patel denied Head a century by hitting the top of his off stump with a ball from the rough but Australia had reached safety by then.
India let batters Shubman Gill and Cheteshwar Pujara to roll their arms just for fun on a track where only 22 wickets fell in five days.
"That was a pretty flat wicket that one," said Australia's stand-in captain Steve Smith.
"It was a really well-fought series. I think we started to play a lot better as the series went on."
Smith led Australia in the last two tests after regular captain Pat Cummins flew home to be with his mother who passed away last week.
Virat Kohli was adjudged player-of-the-match for his painstaking 186, his first test hundred since November 2019.
Indian spinners Ashwin and Ravindra Jadeja, who claimed a combined 47 wickets, shared the player-of-the-series award.
