After Joe Root's superb 160 helped England to 384 on day two at the SCG, Head led Australia's response with an unbeaten 91 from 87 balls with the hosts 2-166 at stumps.
The star of the summer with the bat, Head hit 15 boundaries and looked set for a century inside a session before nightwatchman Michael Neser shut up shop.
Still, it was another brutal reminder of Head's impact, after his 69-ball century in Perth and 170 in Adelaide helped set up Australia's series winning 3-1 lead.
Head's runs came as part of a 105-run second-wicket partnership with Marnus Labuschagne (48), who was also involved in the flash point of the final session.
With light fading, he and Ben Stokes exchanged heated words, with the England allrounder putting his arm around Australia's batter.
Stokes' ultimately won out, dismissing Labuschagne with the next ball he bowled at the Queenslander by having him caught in the gully.
Jake Weatherald was the other Australian out Monday, trapped lbw for the fourth time this series on 21 after a quickfire 57-run opening stand with Head.
Weatherald's dismissal to Stokes (2-30) will raise questions over his long-term future, given his 72 in Brisbane is his only score above 25 for the series.
But there are no questions over Head's spot in the side, with the case for him to stay at opener rather than No.5 only being strengthened.
The 32-year-old has now passed 500 runs for a series for the first time in his career, doing so at a strike-rate of 87.12.
"Every ball he is looking to score," Neser said.
"He is not trying to work it around or grind it out. He is looking to score every chance he gets.
"And most times he creates more opportunities than normal batters, because he is so talented."
Head's ability to put the pressure back on England was also aided by terribly wayward bowling early from Matthew Potts and Brydon Carse, who were both far too short.
Potts was particularly poor in his first Test of the series, giving Head the chance to cut and pull before finishing the day with 0-58 from seven overs.
England's new-ball pair also handed Australia easy runs when they returned later in the session, this time bowling too full as Head and Labuschagne feasted on the cover drive.
Earlier, Neser took 4-60 for Australia to kill off any hopes of England reaching 400 for the first time this series.
Well down the pecking order before Australia's injuries this summer, Neser now has 14 wickets at 17.42 for the series after featuring in three of the last four Tests.
He claimed a spectacular caught-and-bowled to remove Root on 160, with the Queenslander largely engineering England's fall from 6-375 to all out for 384.
"Cricket is a funny game," Neser said.
"Once you get into a rhythm of things and start taking wickets, it flows. But I've been on the other end where you can't take a wicket.
"So you take the good with the bad."
After Scott Boland and Mitchell Starc struck early on Monday to dismiss Harry Brook (82) and Ben Stokes for a duck and leave England 5-229, Root took charge.
His 41st Test century - and second in Australia after breaking his long wait last month in Brisbane - came with a flurry of cover drives without the edges behind that have stunted his tour.
But while Root provided the brains of England's innings, keeper Jamie Smith lost his at the other end with one of the worst dismissals of the summer, on 46.
With lunch in sight and England 5-323, he inexplicably hit a short ball from Marnus Labuschagne straight to deep cover.
In doing so he cruelled England's chances of a massive total, after already being handed two lives on 24 after after being caught on a Cameron Green no-ball and edging the next delivery through the slips.
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