With Australia now firmly on the front foot in Sydney, Head became the first Australian opener in 23 years to post three centuries in an Ashes series.
After resuming on 91no, the South Australian continued his brutal assault on England's bowlers on Tuesday to go to lunch unbeaten on 162.
His innings has helped Australia to go after a win in the fifth Test for a 4-1 series victory, with the hosts now just 103 runs off England's first-innings 384.
In a miserable opening session for the tourists, they burned both remaining reviews trying to rid of nightwatchman Michael Neser.
Neser was eventually out for 24, but by that point he had batted for more than 100 minutes on day three and taken the sting out of England's attack.
Will Jacks also spilled a simple chance to dismiss Head on 121, after the left-hander pulled a Brydon Carse ball straight at him on the legside boundary.
But this has been the story of England's summer, with Zak Crawley and Jacks also grassing tougher chances against Steve Smith (16no) and Head just before lunch to make it 16 drops for the summer.
Another ongoing issue has been their lack of answers for Head, with fields set deep for most of Tuesday.Â
He brought up his century from 105 balls with 24 boundaries to his name by lunch and one big six over the legside off Matthew Potts.
While questions remain over Australia's opening pairing after Jake Weatherald's wasted start on Monday, Head's move up from No.5 is now entirely vindicated.
Australia have indicated they will re-evaluate whether Head should remain as opener at the end of this summer, or move him back down the order.
But it's hard to see the opening experiment being abandoned after a 69-ball match-winning century in Perth and big 170 in Adelaide.
By reaching his third century of the series on Tuesday, Head became the first Australian opener to do so in an Ashes battle since Matthew Hayden in 2002-03.
The 32-year-old, who was only moved to the top of the order in the second innings of the first Test due to Usman Khawaja's back injury, already has the most runs in a series by an Australian opener this century.
Head made Potts his prime target at the SCG, feasting on wayward bowling from a quick who has been too short and bowled both sides of the wicket.
The left-hander took 65 runs off the 47 balls he faced from the seamer, smashing nine boundaries and the big six in a brutal welcome back to Test cricket.
Playing his first Test in more than a year after England lost three frontline quicks to injury on this tour, Potts went for 0-104 off 17 overs.
