Head hits back for Australia after Root's majestic 160
Root's superb innings, his 41st ton to match Ricky Ponting, was only ended courtesy of a brilliant caught-and-bowled by Michael Neser, who finished with 4-60.
Australia were left to negotiate the final session of day two at a sold-out Sydney Cricket Ground, which they did for the loss of Jake Weatherald (21) and Marnus Labuschagne (48).
By stumps the hosts -- who have already won the series -- had raced to 166-2 with nightwatchman Neser on one alongside Head.
"I think it's set interestingly," Root told TNT Sports.
He added: "Most important for us is not panicking, not dwelling too much on what happened here.
"It's how we respond tomorrow morning and maximise that chance first up."
Weatherald, who needed a big score to stave off the critics, again failed to live up to expectations since making his debut at the first Test in Perth.
He was dropped twice in the space of three balls, by Root then Ben Duckett, before Ben Stokes trapped him lbw.
But Head, who like Root has slammed two centuries this series, was in the zone.
He clattered three boundaries off the second over from Matthew Potts, in the side for the injured Gus Atkinson, and there was no let-up, blitzing a quickfire 50 off 55 balls.
Labuschagne was also in good touch, stroking seven boundaries before thick-edging Stokes to Jacob Bethell at gully.
Labuschagne and Stokes had clashed between overs, with the England captain aiming an expletive at the batsman.
The hosts lead the series 3-1 and have already retained the Ashes, with England desperate for another win after victory at the previous Test in Melbourne.
"Fresh start tomorrow," said Neser.
"But the wicket seems to be quickening up just a little bit, so we're going to be mindful of that tomorrow."
Root joins Ponting
England resumed at 211-3 but lost Harry Brook (84), Stokes (0) and Jamie Smith (46) before lunch.
Will Jacks (27), Brydon Carse (1) and Josh Tongue (0), along with Root, departed in the second session.
The day belonged to Root, who started on 72 and reached an almost chanceless century off 146 balls to reaffirm his status as an all-time great.
The 35-year-old had begun the series under pressure after failing to make a hundred in Australia over three previous Ashes tours.
He snapped the drought with an unbeaten 138 in the day-night Test at Brisbane and his exploits in Sydney drew him level third with Australia's Ponting on the all-time century-makers' list, with 41.
Only India's Sachin Tendulkar (51) and South Africa's Jacques Kallis (45) have scored more Test centuries.
Root and Brook came together with England in trouble at 57-3 on Sunday, with both eyeing big centuries on an ideal batting deck.
But Brook only lasted five balls on Monday, adding six to his overnight 78 before dabbing at a Scott Boland delivery and edging into the safe hands of Steve Smith at slip.
It ended a 169-run partnership, not just England's best of the series but the biggest by either team, surpassing Head and Alex Carey's 162 in Adelaide.
Stokes only survived 11 balls before getting the faintest of edges off Mitchell Starc to Carey.
Jamie Smith lived dangerously and was fortunate to survive after chipping Cameron Green to Labuschagne at cover on 22. He began walking off but replays showed Green overstepped and it was a no-ball.
He added another 24 before medium-pacer Labuschagne bagged him in his first over.
The run rate slowed significantly after lunch when the new ball was taken, but Root persisted, passing 150 for a 17th time, just one behind the legendary Don Bradman and three short of Tendulkar.
He and Jacks put on 52 for the seventh wicket until Jacks sent a leading edge to Green in the gully off Neser. Root was ninth man out and Tongue followed without any addition to the score.