Bora Milutinovic's team needed to register a win and wait for Spain to beat South Africa to qualify to the next phase.
While Spain did their part by defeating the competition's hosts 2-0, Iraq could only produce a lame display where they failed to even threaten the All Whites.
The game witnessed very few chances from both sides and surprisingly New Zealand, who had no chance of reaching the semi-final were the better side.
Iraq's first presence of the game came when Emad Younes was released by Emad Mohamed before Glen Moss rushed off his line to deny the former.
New Zealand put their opponent under pressure and Chris Killen had a good chance but his effort from inside the box went wide.
Striker Shane Smeltz saw his header go wide after a left-wing cross from Leo Bertos.
New Zealand controlled much of the possession after the interval.
However, Iraq had one final chance to win the game but Karrar Jassim's shot came off Moss's head and bounced away from the danger zone.
The draw is New Zealand's first ever clean sheet in their third Confederations Cup participation.