India had been undefeated throughout the tournament but were bowled out for 240 on the final ball of their innings before Head starred for Australia on his way to a match-winning 137 — after Australia had been reduced to 3-47 in front of an increasingly frenzied home crowd.
Head, with able support from Marnus Labuschagne (58), steadied the ship to lead Australia to victory despite falling with just two runs required.
He became the third Australian to make a century in a men's world cup final, joining Ricky Ponting (2003) and Adam Gilchrist (2007) in doing so.
The opener, who was also player of the match in Australia's semifinal victory over South Africa and in the World Test Championship final at The Oval earlier in the year, had earlier taken a difficult diving catch to remove dangerous India captain Rohit Sharma for 47 off 31 deliveries, just as he threatened to take the match away from Australia early.
While that dismissal off the bowling of Glenn Maxwell laid the platform for Australia to rip through India's middle order, it was what Head did with the bat that ultimately decided the match.
His innings was the measured stuff of a matured master, albeit one who had never thought he would be in this situation, after a fractured hand threatened his very involvement in this World Cup.
Opening partner David Warner described Head's comeback as "magnificent", his captain Pat Cummins called it the ultimate gamble from Australia's selectors.
"What an incredible comeback from Heady," Warner said.
"Injured in South Africa — to come back and score a hundred in his first game back and then hit a hundred here tonight in front of a jam-packed crowd is absolutely phenomenal."
Cummins could not quite believe it.
"It's amazing and I thank the unheralded few … the selectors that backed him in and the medical team to get him back," Cummins said.
"It was a big risk and it paid off."
Against India, Head's wicket was threatened early and often as opening bowlers Jasprit Bumrah and Mohammed Shami hooped the ball around and moved it off the seam in slick night-time conditions.
Warner barely survived Bumrah's opening over, edging one through the slip cordon, but the signs were more positive for Head and a harbinger of things to come as he twice crushed India's opening quick through the off side for boundaries.
However, Warner was gone the next over, nicking one off Shami to be caught at slip by Virat Kohli for seven.
Mitch Marsh came in and immediately went after the pair and, even though he looked to be in good touch, he nicked a straight ball from Bumrah to be caught behind for a run-a-ball 15.
Steve Smith came in to help right the ship but he too struggled and when Bumrah rapped him on the pads with a big shout, Smith was given LBW.
The former captain, who is often fond of a review, decided against sending the decision to the TV umpire, but replays showed he had been hit outside the line of off stump and would have earned a reprieve.
It could have been a turning point with Australia 3-47 down but in the end, it was just a curious footnote.
Head was subsequently joined at the crease by Marnus Labuschagne and the pair made sure it did not matter.
The duo were forced to stave off the Indian quicks as the ball continued to move and, while Labuschagne is usually happy to drop anchor, Head, who loves to be the aggressor, also had to dial it back to give Australia a chance.
From the end of the seventh over, when Smith was removed, to the end of the 17th over, Australia made just 50 runs as the pair looked to settle. Of those runs, the ever-watchful Labuschagne added only 10.
But it was just what was needed.
Head passed his 50 and began to unleash the shackles ever so slightly as Australia's confidence grew and the required runs came down, but in the 28th over disaster almost struck.
Labuschagne was rapped on the pads by Bumrah, right on the Kookaburra logo, and India reviewed the not-out decision.
DRS showed the ball thumping into a pretty big part of leg stump but not enough for it to be overturned.
That was truly India's last gasp as Head, already on 80, soon began to accelerate the run rate.
It took him a few overs but he eventually went after Kuldeep Yadav and brought up his hundred with 11 off the 34th over as Australia closed to within almost 50 of the total.
From there, Head began to clear the boundary with more regularity, finding the rope with increasing ease as he threw caution to the wind, while Labuschange nudged his way towards his 50.
It seemed Head would carry his bat just like Gilchrist did in 2007, before he finally holed out when trying to whack Mohammed Siraj to the boundary with just two runs needed.
It did not matter, as Maxwell came in and immediately hit the winning runs.
Ever one to play his own role down, Head indicated he did not believe he was in the class of Gilchrist or Ponting, even though he was elated.
"I'm definitely third on that list. It is a nice one to join," Head quipped of Australians who have made a ton in a World Cup final.
"I couldn't imagine getting a hundred or holding on to that one [catch that dismissed Sharma] … it's nice to hold onto something this important."
He then paid tribute to Labuschagne after the pair put on 192 for the fourth wicket.
"I was a little bit nervous but Marnus played exceptional," Head said.
"It was awesome to bat with him, he soaked up all the pressure and it was an amazing partnership."
Labuschange, who thought he may have been dropped for the match, and only found out he was in after Australia's coaches examined the pitch the night before, was equally effusive in his praise.
"Travis put on a hell of a display and it was great to be a part of it with him," he said.
Pace trio set up victory
The victory may have been delivered by a batsman but it was set up by the Australian pace brigade.
When Cummins won the toss and elected to bowl, the decision surprised plenty and it had appeared to have backfired badly early as Sharma and Kohli looked to be in good touch with India cruising at 1-76 before Sharma was dismissed.
And while Shubman Gill and Shreyas Iyer went cheaply to leave India 3-81, it had seemed Kohli and KL Rahul had steadied India's ship.
Then came the big wicket, as India's talisman and the man who scored the most runs this World Cup, Kohli, played a horizontal bat to a Cummins bouncer and chopped the ball onto his own wicket.
Kohli, later crowned Player of the Tournament, looked on in disbelief at his dismissal for 54 as Cummins (2-34) leapt for joy.
Rahul was left to try and rescue India and his steady 66 was their top score but, when he fell after edging Mitchell Starc (3-55) to Josh Inglis, India were 6-203 and in trouble.
Josh Hazlewood got both Suryakumar Yadav and Ravindra Jadeja, while Starc took the wicket of Shami as Australia's pace trio took seven of the 10 wickets.
Cummins's decision to bowl had been vindicated and he said he was relieved.
"Tonight, we thought it was a good night to chase down … we thought it [the pitch] might get a bit easier to play later," he said.
"I thought everyone adjusted pretty well and bowled some tight lines."
That they did, as they handed a shocked India a loss they never expected and Sharma said Australia made all the right moves.
"Honestly, we were not good enough today," he said.
"We tried everything we could, but the wicket got slightly better to bat under lights."
Story first published on ABC News