Australia have come within a whisker of a Bledisloe Cup upset win in Wellington, instead settling for a 16-16 draw in their first Test under new coach Dave Rennie.

Huge underdogs against the All Blacks after a squad overhaul, a fortnight in quarantine and 23 matches without a win on Kiwi soil, the Wallabies led with just three minutes remaining on Sunday.

Marika Koroibete and debutant Filipo Daugunu went over for second-half tries as Australia clawed back a 10-point deficit and went ahead through a James O’Connor penalty.

The Wallabies stirring performance almost earned the result it deserved when Reece Hodge stepped up for a snatch victory with a 54m penalty shot after fulltime.

Unfortunately Hodge’s monster kick crashed against the upright, cruelling hopes for a drought-ending victory.

“We had our chances,” Rennie said ruefully.

Play continued for nine additional minutes, with both sides coming within metres of scoring in a barnstorming finish.

Like many fans among the 31,020 or screaming at their television, Rennie said he didn’t know why someone didn’t step up for a drop goal.

“We practised it during the week … I’m not sure what happened around the communication. An opportunity lost,” he said.

O’Connor, who kicked two out of four efforts, finally ended the spectacle by booting the ball into touch for the draw.

Wallabies skipper Michael Hooper, playing his 100th Test, said there was a lot to like about their performance.

“I’m very proud of our team to fight all the way through,” Hooper said.

“Despite the conditions and despite the result, we are off to a good start with some things … there’s a lot of belief.

“It was close – a kick off the post – but we’ll go again next week.”

The All Blacks weathered early Australian pressure to score the first try in the ninth minute after officials missed Rieko Ioane’s foot on the sideline before Jordie Barrett scored.

Karmically, Ioane missed the chance to score on halftime as he botched the grounding of a breakaway try under no pressure.

O’Connor missed a kick to bring the scores to 8-6 just after halftime and within minutes the Wallabies trailed 13-3 when Aaron Smith wriggled free of Nic White’s desperate defence to score.

Australia finally went over through Koroibete’s desperate lunge in the 53rd minute.

White’s brilliant flick allowed Daugunu a try in his debut Test, levelling the scores at 13-13.

O’Connor kicked a penalty in the 73rd minute to break the deadlock, which looked like it could be enough for Australia to win in New Zealand for the first time since 2001.

But veteran Australian lock Rob Simmons gave away a penalty with two minutes remaining, allowing All Blacks winger Jordie Barrett to level.

The Wallabies head to Auckland’s Eden Park on Sunday for the second Test, and will do so full of confidence after the spirited showing against the odds.

All Blacks coach Ian Foster, in his first game as senior New Zealand coach, couldn’t hide his frustrations.

“Heck of a game … congratulations to Aussie on a really tense Test match,” he said.

“It’s bitterly disappointing from the All Blacks side but it’s a start.”