Australia crashed to 3-12 in 10 overs on a green pitch after losing the toss, reliving their nightmarish start to the previous Test at Bellerive.
But there was no meek collapse to rival the chaos of 2016.
Instead, a counter-punching Head humbled England's beleaguered bowlers with help from Marnus Labuschagne and Cameron Green.
Head will be kicking himself after falling for 101, chipping a catch to Ollie Robinson immediately after celebrating his second hundred of the five-Test series.
The left-hander, forced to miss the SCG Test after contracting COVID-19, nonetheless shifted momentum in a staggering fashion that belied Friday's opening hour in which pink ball dominated bat.
Head shared a 71-run partnership with Labuschagne, which ended in bizarre fashion in the penultimate over of the opening session, then a 121-run stand with Green.
The Head-inspired comeback was the latest reminder of Australia's depth this summer, coming after recalled paceman Robinson removed David Warner and Steve Smith for ducks in an inspired opening spell.
It marked the first time that Warner and Smith both failed to trouble the scorers in a Test innings.
Green was unbeaten on 57 while Alex Carey was one not out going into the final session.
Head cracked 12 boundaries, overtaking Labuschagne as the series' leading run-scorer in the process.
Robinson, who trudged off to the change rooms because of a sore back but returned to field, has only delivered eight overs.
An exasperated Joe Root, who demanded better from teammates as England lost their grip on the contest in the opening session, will be desperate for Robinson to return to the bowling crease.
Australia weren't without luck; Labuschagne should have been dismissed for a duck during the early carnage.
Robinson found Labuschagne's edge in the eighth over, only for second slip Zak Crawley to dive in front of Root and grass the catch.
Labuschagne's not-so-fancy footwork later brought about his downfall.
The world's No.1 Test batter tried to give himself room by stepping to the off side but slipped over, with Stuart Broad's delivery hitting middle stump.
13°C