Could they dig Australia out a hole when Steven Smith, David Warner, and Marnus Labuschagne missed out?
Entering at 12 for 3 and 83 for 4 respectively, on a Bellerive pitch that looked as green as the outfield, Australia's least experienced batters and their two project players prospered under pressure, sharing a 121-run stand to confirm their places as key pillars in the team.
Head's 101, his fourth Test century, was arguably better than his blitzkrieg in Brisbane. As good as his 85-ball century in a session was, he rode his luck and benefitted exponentially from the earlier work Warner and Labuschagne.
Green matched his 74 in Sydney where he was shepherded through by Usman Khawaja. He deserved a century in Hobart but fell to his only real mistake in his most assured Test innings. His class and composure showed his belief is growing, and that he is every bit a top-six batter in Test cricket.
Their performances were significant in the context of a bizarre day. For the first time in 128 Test innings and 244 international innings in all forms, Smith and Warner both fell without scoring. The other senior pro Khawaja, coming off twin centuries in Sydney, also nicked off for 6.
Labuschagne should have also departed for a duck, dropped yet again by Zak Crawley at second slip off Ollie Robinson.
Australia haven't made 300 without at least a half-century contribution from one of Smith, Warner or Labuschagne in 21 Test matches since February 2019, when Head made his maiden Test century on a magnificent Manuka Oval batting strip against Sri Lanka.
But this was an experienced England attack with their tails up in English-style conditions, and at a ground where he averages just 19.28 in the first innings in Sheffield Shield cricket. Head produced a swashbuckling counterattack that ripped the momentum from England's grasp in no less than three hours.
He was the recipient of some really poor bowling. His first three boundaries came from three long half-volleys. Mark Wood bowled two bouncers and hit him twice, but never peppered him again. He instead feasted on full balls and latched onto width.
Head and Labuschagne pilfered 71 runs in 12 overs. The pair had flashbacks to their respective lean trots in last year's County Championship and decided the best form of defence was attack. Labuschagne finally paid a price for his inventive footwork, literally falling flat on his face and being bowled around his legs by a straight half-volley for 44 in possibly one of the most bizarre and amusing dismissals ever seen in Test cricket.
It brought Green to the crease at 83 for 4 in the 23rd over. It was just the fourth time in Test cricket he had entered with the team total under 100. He has scores of 74, 74 and 45 in three of those innings - with the fourth having come on his debut in Test cricket - and has shared in two century stands and a half-century stand in them. Despite his incredible all-round skill set, at his core he is a top-order batter. He can't handle watching and waiting, having been a top-order batter for most of his life. In his first first-class century batting at No. 8 for Western Australia, he entered at 50 for 6 in the 28th over. In first-class cricket he averages 63.55 at No. 4, 86.00 at No. 5 but just 36.20 at No. 6 and 25 at No. 7.
In Hobart, he was in his natural habitat, against a newish ball early in the game. The nervous pushes and prods, and the trembling footwork patterns that had been forensically examined in the first four Tests were nowhere to be seen.
He provided the perfect foil to Head, stroking some glorious cover drives to get his innings going and rotating the strike well.
Head clicked up a gear after the first break. Robinson, battling a back injury, floated up a 112kph half-volley and Head flicked it contemptuously over midwicket. He continued to plunder anything overpitched as the pair rattled along at four an over. Head noted after his innings that rotation of strike was important on that surface as a left-hand-right-hand combination. Head's decision-making was also a feature. He told Channel Seven that he had put a higher price on his wicket in nets practice at training.
"I haven't traditionally been the best net batter in the past and it's something that I've worked really hard on, being hard to get out in the nets," Head said. "Over the last two days, I was really conscious of making sure that I was making the right decisions, moving on the right balls, attacking the right ones, defending the right ones, and being hard to get out. I felt like I had come into this Test feeling ready to go."
His century seemed an inevitability, as opposed to some of his previous high-wire acts, where one false step looked moments away. Although he did nearly spoon a catch on 99. And after caressing a two to third man to bring up his ton, he reverted to type, chipping a cutter from Chris Woakes needlessly to mid-on.
Green also looked odds on to make his first Test century, cruising to 74 with some superb strokes off the front and back foot off the pace of Wood in particular. But the bouncer barrage that wasn't bowled to Head was finally delivered to Green with a leg-side trap in place. Green fell for it hook, line and sinker. He was rattled by a couple of quick short balls but rode them well. Wood went around the wicket and delivered the shortest and widest bumper of the lot. Green took on the pull and roped it straight down deep square's throat.
Both dismissals showed neither Head nor Green are the finished article. But Head is now this Ashes' leading scorer with two centuries and a fifty, averaging 69.80 at a staggering strike rate of 87.46, while Green has two vital scores of 74 to go with his nine wickets at 15.44. Along with Khawaja, they have been Australia's stand-out domestic batters for the last two years and are now starting to prove their mettle at Test level.