Reece Hodge had the chance to snatch a win with a 55-metre penalty goal attempt after the full-time siren, but his shot hit the right-hand upright.
Play continued but neither side was able to find the winning points, with James O'Connor finally electing to boot the ball into touch and settle for the draw almost nine minutes after the siren had sounded.
O'Connor kicked a penalty in the 63rd minute to split a 13-13 deadlock and it looked like it could be enough for the Wallabies to break through for their first win over the All Blacks in New Zealand since 2001.