Dan Carter missed a drop goal attempt in the 85th minute which would have clinched a late win for the All Blacks in a try-less test.
The world champions, chasing a record-equalling 17th straight victory, had a chance to steal the spoils in an extraordinary end to the contest but Carter, who kicked six penalties, steered the ball wide right of the posts.
Australia, whose points came from five Mike Harris penalties and a long-range effort from Kurtley Beale, also had a chance to win the match after time was up, only to be penalised as they went through the phases looking for a penalty of their own.
Rather than kick the ball out to end the match, though, the All Blacks took a scrum and forced their way back into range for Carter's attempt, a decision that disappointed coach Steve Hansen said showed "huge" character.
"It was probably one of the ugliest games of rugby I've seen," he told reporters. "We're really, really disappointed, too many avoidable penalties, too many avoidable mistakes.
"But to play as poorly as we did and still manage to show the character and tenacity to get the draw was pleasing. It's not the end of the world but there's enough pain and hurt in the dressing room to make sure we learn the lessons from it."
The All Blacks were uncharacteristically error-prone on what was a greasy surface at Lang Park but the Wallabies were also frustrated at not coming away with the win, despite starting the match as 6-1 underdogs.
"I expect the boys will be pretty disappointed because that's a game we could have won," said coach Robbie Deans.
"But to put ourself in the position to win their game and to hold that All Blacks side tryless is a significant achievement."
Captain Nathan Sharpe, playing his last match on Australian soil before retirement, was the heart of a Wallabies team that contributed to the All Blacks error count by putting immense pressure through a spirited performance.
The All Blacks had opened the proceedings with the "throat-cutting" version of the haka in honour of hooker Keven Mealamu's 100th test cap but the Wallabies soon made it clear they were not going to play to the visitors' script.
Fullback Harris gave them the lead after just two minutes when the All Blacks were penalised for not rolling away from the tackle area.
Carter made no mistake with his first two penalty attempts to give New Zealand the lead but nine more points from the boot of Harris gave the home side an unlikely lead.
All the offenses were in the tackle area and referee Craig Joubert warned All Black captain Richie McCaw after the third that he would sin-bin the next offender.
The South African was true to his word and prop Tony Woodcock was shown the yellow card a minute before the break with the home side 12-6 ahead.
Woodcock had just returned when Beale boomed a penalty over from inside his own half to extend the lead to 15-6 but Carter, who had missed his two previous attempts, narrowed the deficit with two penalties in the next six minutes.
The latter offense had caused Wallabies flanker Michael Hooper to be sin-binned for tackling Aaron Smith off the ball and it looked like the All Blacks might impose themselves on the contest.
Carter duly levelled and put them ahead with his sixth penalty 10 minutes from time but the Wallabies hit back with Harris's fifth to set up the dramatic climax and just the sixth draw in tests between the nations.
The match was the third test in the Bledisloe Cup series, which the All Blacks won courtesy of their victories in the first two tests of the Rugby Championship.
A victory at Lang Park would have allowed the All Blacks to match the New Zealand team of the late 1960s and South Africa side of the late 1990s in being the only top-tier teams to have won 17 straight matches.
Hansen was more bothered by a headbutt by Australia flanker Scott Higginbotham on his captain McCaw.
"Another cheap shot on the bloke, he seems to get it every week, and everyone seems to miss it," he said.
