A lengthening afternoon, an Adelaide Test, and two South Australians batting together in the sunshine. Something felt very right about that, as Travis Head and Alex Carey took Australia towards a first-innings lead of 157 against India through much of the second session of day two. The old scoreboard ticking, the church steeple peering over the grandstand’s shoulder, the hill stuffed like a French goose, the people in a sell-out crowd robustly voicing approval as Head in particular kept whacking a pink missile in their direction.

In practical terms, state-based parochialism is irrelevant in modern Australia, a performative dance for politicians to half-heartedly perform around budget allocations or State of Origin. Even with cricket’s domestic structure still built along those borders, the consensus from outside South Australia admits that Adelaide Oval is the country’s best ground, and Adelaide’s Test the summer’s most enjoyable. The festival feel is unique, the city always turns out. Even among grumbling at being allocated the struggling West Indies the past two summers running, Adelaide cracked 50,000 people over the first two days both times. For the same team, Perth didn’t get that many in five.

Related: Australia v India: second men’s cricket Test, day two – as it happened

So South Australia is probably entitled to a few more years of chips on shoulders when it comes to the Test side, with so few representatives for so long. Since the Chappell name moved from the scoreboard to a grandstand, the picks got slim. We saw Tim May ring the bell to start this Test; he bowled off-spin in a difficult era, and was the not-out scrapper here when West Indies won by a run. Greg Blewett had his moments, Darren Lehmann a stint, Jason Gillespie a substantial career. But if a South Australian played they were usually on their own.

In this current moment, with bigger stars fading, Head and Carey are the most important axis of Australia’s batting. Both are born and bred South Australians. A third member has recently joined, the state captain, Nathan McSweeney, opening the batting, and while he is from Queensland he has raised his game in his adopted state. The home cartel might even partially claim a fourth member, with Nathan Lyon’s Test ascent having relied on his move to South Australian domestic cricket all those years ago.

So to come back around, it felt right. The two most local picks doing the job when Australia needed it, reward on the field for Adelaide’s people and the South Australian Cricket Association having made this event such a pleasure over years of effort.

The national team were in jeopardy when Carey joined Head at the fall of the fifth wicket. It had felt as if things were going well, with two players under pressure performing: McSweeney by grinding out 39, mostly on the previous evening after Usman Khawaja fell, before the implacable Jasprit Bumrah’s movement off the seam drew a nick; then Marnus Labuschagne climbing out of his rut with an increasingly fluent 64 before poking a catch to gully looking for runs.

But Steve Smith stayed in his own rut by nicking down the leg side for two, Mitchell Marsh edged a lovely straight break from Ravichandran Ashwin on nine, and at five down Australia were 28 runs ahead of India’s 180. More wickets in quick time and the eventual lead might have been something very easily overtaken.

When Head is at the crease, more wickets in quick time look entirely possible. He threw the bat at wide balls that he might have chopped on, flashed through gully and, when the field shifted around for a bouncer attack, edged through a new gap between keeper and second slip with both fielders watching the ball go by in mortification. He scorched Ashwin over long-off for six, then tried to double down next ball, skying a slog sweep into the leg side. Mohammed Siraj’s Superman dive couldn’t cling on to the mid-air catch.

But somehow, as he has kept on doing, Head made it work. He is counterintuitively consistent despite his approach. A few recent first-ballers notwithstanding, he has a low proportion of single-figure scores, with fast starts meaning that most times he at least makes something of moderate substance. Eight centuries in 51 matches is a good return, as is an average over 43.

As they all have been, this one was fun to watch. Three sixes from Ashwin, and a late one from Siraj flicked over square leg. Drives down the ground or through cover with crunching power, few players doing as Head does in trying to hit the thing so hard its atoms vibrate it into a side dimension. The sound of impact ricocheted into the outer, the crowd’s exulting coursed back the other way – it was a virtuous cycle, an Adelaide feedback loop. Meanwhile, Carey dabbed and dropped, only needing 15 himself to add 74. When he nicked off the lead was 102, the tail with Head had licence to whack a few more, the approaching evening session looked like the best time to bowl, and it delivered with venom on that promise.

Head got cleaned up on 140 trying to pulverise a yorker, Siraj by now so frustrated that he launched into a send-off, Head throwing back a rebuke as unsubtly as he had just thrown the bat. But spectators kept getting their money’s worth: Mitchell Starc curling the pink ball again, Scott Boland continuing his mystical run of first-over success, Pat Cummins producing another perfect decapitation of an opposing captain, and Rishabh Pant smiting shots on the counter.

Head is a good-fortune indicator: after each of his previous seven centuries, Australia have won the Test. This time, with India five for 128 and 29 runs behind, his team have every chance to make that eight from eight. If they don’t, it will be due to an Indian miracle. If they do, the only downside for Adelaide is that Sunday, at 26 degrees and clear, might be a short day at the cricket.