The world champions trailed for long periods in the final Bledisloe Cup match of the season and were 15-6 behind with just 30 minutes remaining.
Dan Cater converted four successive penalties to give the All Blacks a three-point lead just five minutes from time.
Mike Harris responded for the Wallabies to level the scores, forcing New Zealand to go for broke in the closing stages.
Carter attempted a drop-goal in the final few seconds to try to snatch victory but his effort drifted wide to leave the scores deadlocked.
The draw means that New Zealand failed to match the efforts of South Africa in 1997-98 by the narrowest of margins.