Australia head coach Dave Rennie said the Wallabies are disappointed after coming within a whisker of snapping their New Zealand hoodoo as the Bledisloe Cup opener ended in a dramatic 16-16 draw.

Reece Hodge had the chance to secure Australia's first win in New Zealand in 19 years and first in Wellington since 2000, but the replacement back's monster kick from inside his own half hit the post in additional time on Sunday.

The Wallabies ushered in a new era under Rennie – overseeing his first match in charge since replacing Michael Cheika, just like All Blacks counterpart Ian Foster – rallying through second-half tries from Marika Koroibete and debutant Filipo Daugunu, having trailed 13-3 to Jordie Barrett and Rieko Ioane five-pointers.

And Hodge almost snatched an incredible victory in the 83rd minute after the full-time siren sounded, however, his long-range kick cannoned off the woodwork in wet conditions at Sky Stadium, where James O'Connor eventually kicked the ball out of touch following nine thrilling extra minutes.

"We're disappointed," Rennie told reporters in his post-match news conference. "We're certainly not celebrating in the changerooms.

"We had our chances. I thought we played with a lot of courage."

"We let ourselves down," added Rennie, addressing the breakdown, though the Wallabies won nine turnovers – only the second time in the last decade they have won more in a Test against the All Blacks.

"We found a lot of space in behind them, we had a lot of ball but the quality of our cleanout just wasn't good enough and it's area we need to be better next week. We gave away 14 penalties and a big chunk of those were post-tackle."

"I'm really proud. We were under the pump early," Rennie said. "I thought we defended well for big chunks of the game, we were able to apply pressure through our kick game and scored a couple of good tries at important times.

"We had our chance right at the death, one off the post and then setting up of a drop goal and we ended up going wider. They put you through it!

"The quality of our clean out wasn't good enough and they were able to stifle a lot of ball. We knew the collision area was going to be important and they won that battle."

Both Australia and hosts New Zealand were playing for the first time in 2020 amid the coronavirus pandemic, with a strong crowd in attendance to watch the first of four Bledisloe Cup fixtures.

Wallabies captain Michael Hooper made his 100th Test appearance – becoming just the 12th different player to reach the century mark for Australia – and his 47th as skipper.

Hooper led from the front as the Wallabies impressed against their trans-Tasman rivals, after trailing 8-3 at half-time, with Koroibete and Daugunu crossing over, with the latter becoming just the fourth Australia player since the beginning of this century to score a try when their career Test debut has been against the All Blacks, per Opta.

O'Connor and Barrett traded penalties at the death, after Australia had led with 90 seconds remaining, setting up a grandstand finish.

"It was a good start to our year. We haven’t been together for almost a year," said Hooper.

"We've got a new group here and a few debutants tonight. I’m very proud of our team, they fought all the way through. Man, it was close … a kick off the post … but we go again next weekend and hopefully we’re up to the challenge."