Australia may never get a better opportunity to wrest back the Bledisloe Cup than the one they were gifted on Saturday. At home under sunny skies, with a full-strength side, they faced an underpowered All Blacks outfit almost as determined to shoot itself in both feet as they were. Yet the Wallabies still couldn’t get the job done.

To their credit, Australia knew how lucky they were to get to 31-28 at the end. “We got close tonight, but not close enough,” captain Harry Wilson said of a 22nd straight year of Bledisloe failure. The scoreline wasn’t even worth a glass-half-full outlook, growled coach Joe Schmidt. “You lose a Test match, there’s not a lot of water in the glass.”

Related: Wallabies fall narrowly short of All Blacks amid brave Bledisloe Cup comeback

New Zealand butchered seven tries in an hour, four with arrogance or ineptitude and three when the TMO found tiny errors in the lead-up. It was the three tries they did score and the 21-0 lead they amassed in the first 15 minutes that snuffed the Wallabies comeback before it began, paving the way for an embarassingly clumsy Kiwi victory.

“We found a way,” grimaced All Blacks coach Scott Robertson after his side’s first win following back-to-back defeats to South Africa. “The last three Test matches have come down to a pass, a ref call, decision making. That’s Test footy.” Yes, but so too is the reality that Australia have now lost eight straight Tests to New Zealand since 2020.

Robertson’s relief that his men held on despite playing the later stages with 13 men was matched by Schmidt’s pride the Wallabies fought back from 28-7 down. “They were gritty [and] put together some pretty good footy,” he said. “We earned the [points] we got in the first half, then really rolled our sleeves up in the second.”

Schmidt’s real surprise was how diabolical Australia were early. “They went through us pretty quickly,” he said. At least the Wallabies heeded their coach’s plea to “stay connected” in the second half. They emptied the tanks and went down swinging, keeping New Zealand scoreless in the final 33 minutes to win a late sniff at victory.

“There’s some things to be proud about around building our way back into the game,” said Schmidt. “But giving New Zealand a start like that, it’s too tough to overcome.” After 39% possession in the first half, Australia claimed 52% of the second and forced the All Blacks to miss 24 tackles, concede eight turnovers and cop two yellow cards.

This Test flipped the script of the final half-hour from last week. In Santa Fe, Australia dominated most facets of the game, charging to an early ascendency over Argentina and cruising to a 20-3 lead in the first half hour. But they were demolished in the final 30 minutes as Los Pumas ran riot to score nine tries and run up a record 67-27 scoreline.

Having shocked the All Blacks in round one of the Rugby Championship, Argentina beat the world champion South Africa on Saturday. It proves how potent Los Pumas can be and reinforces the Wallabies’ achievement in beating them 20-19 last month. That victory and the Sydney fightback should fuel a belief they can win next week.

New Zealand are at home in Wellington and unlikely to play as poorly as game one. But they have lost form under Robertson and Australia are improving under Schmidt. If Australia can combine the first 30 minutes from Santa Fe with the final 30 in Sydney, they can beat the All Blacks as Argentina did 38-30 at the same venue back in August.

It’s why Schmidt is irked the Bledisloe isn’t a three-match series. “We’d love it to be still alive,” he said. “Wellington, it’s sold out and would be a cracking atmosphere.” A third Anzac Test was briefly mooted and both unions need it to counter the NRL threat but Rugby Australia are leveraging the idea to boost a broadcast deal in 2025.

Related: Argentina stun South Africa to keep Rugby Championship hopes alive

But it’s no use mourning the absence of a decider until you square the series. Schmidt got plenty right on Saturday. His finishers Lukhan Salakaia-Loto and Brandon Paenga-Amosa turbocharged a comeback. The returned Fraser McReight and Hunter Paisami were best afield. And attacking the edges not the corridor worked a charm.

But Australia missed 35 tackles and their lineout fired blanks. Carlo Tizzano’s 62 from 62 hit-rate in the last two Tests was missed. So too the speed of Max Jorgensen who might have finished the breaks Tom Wright created. Veteran props James Slipper and Allan Alaalatoa added little from the pine and Taniela Tupou’s minutes are too few.

With the European Tour nigh and a vital Test against England on 10 November, Schmidt is entering the crucial second phase of his reign as Australian rugby’s saviour. He welcomes NRL gun Joseph Sua’ali’i as a fresh face of hope for long-suffering fans. Maybe it’s time to farewell a few slow horses and let some other colts have a run too.