Australia completed a remarkable eight-wicket win in the quickest Ashes Test of the modern era, resurrecting England's ghosts of tours past.
Within only four hours, Australia went from being on track to a probable defeat to pulling off a famous victory by the end of play on Saturday.
Australia needed to make the biggest total of the match to win, but Head did it with ease as he blasted England's express quicks to all parts of Perth Stadium following his unexpected promotion to opener.
Chasing 205, Head mowed down the total in blistering fashion, Australia's run-rate ended up at 7.23 when victory was secured.
Player of the series when England last toured, Head smashed his 10th Test century from only 69 balls - the fastest fourth-innings ton in history and equal third-quickest by an Australian, only behind Adam Gilchrist and Jack Gregory.
With just 13 runs needed, Head was finally out for 123 from only 83 balls when he was caught on the boundary off Brydon Carse's bowling.
Stand-in captain Steve Smith, arguably Australia's best batsmen since Don Bradman, said it "had to be right up there" when asked if it was the best innings he had seen.
"Wow. That was incredible to witness," Smith said.
"Trav took it on and played one of the great Ashes knocks."
Legendary Australia captain Ricky Ponting was in awe when commentating on the Seven Network.
"There are so many massive Ashes moments but I'm not sure I've witnessed many, if any better than what I've seen today."
England great Stuart Broad, also speaking on Seven, believed it was "one of the greatest Ashes innings of all-time".
Only one other player, Harry Brook (52 in England's first innings), had scored a fifty in the match before Head's famous knock.
Head's move from No.5 to partner debutant opener Jake Weatherald only came about because veteran Usman Khawaja continued suffering the back spasms that kept him off the field on Friday.
The 31-year-old opens in white-ball cricket, and has done the job in Tests in Asia, but Australia have been reluctant to use him there at home.
Cruising at 1-65 with a lead of 105 just after lunch on day two, England looked headed to snap a 15-Test winless streak in Australia dating back to January 2011.
But England suffered a crushing collapse of 6-39 during an 11-over period, losing 9-105 during the second session to be out for 164 in 34.4 overs.
Their two innings in the match lasted just 67.5 overs, making it the quickest they have been bowled out twice in any Test since 1904.
"It was obvious to us as a group when Travis came out at the top of the order there with Jake that they'd sent Travis out there to play the role in which he's been successful at doing," Stokes said.
"It was so hard to be able to continue with plans in which we tried to implement because he had an answer for everything.
"We went through three, four, five different modes to try and get the wicket of Travis because we knew that he was going to be the big one.
"At the moment, still in a little bit of 'wow' phase after what Travis had just done to us.
"A pretty incredible, special knock from Travis."
Australia exploded out of the blocks, particularly given the first three innings of the match had started 1-0 for the first time in Test history.
Head and Weatherald, who was out for a second-ball duck in the first innings, took England's quicks on with a rapid-fire 75-run opening partnership.
Weatherald, who was cheered when he finally got off the mark, was out for 23, but the recalled Marnus Labuschagne (51 not out) was the ultimate wingman for Head.
Smith arrived at the crease to help Labuschagne tick off the remaining runs.
Star Australia quick Mitchell Starc achieved a 10-wicket match haul for the third time in his career, adding three second-innings scalps after his career-best 7-58 on Friday.
Starc, who led the bowling attack in the absence of captain Pat Cummins and Josh Hazlewood, pipped Head for player-of-the-match honours.
In frightening news for battered England, Cummins is a strong chance to return for the second Test at the Gabba.