The intercontinental playoff is held on a home-and-away basis. The All Whites were beaten 9-3 by Mexico for a place at the 2014 World Cup.
They lead their group with four points after a win (2-0) and a draw (0-0) with New Caledonia in the last few days. They play Fiji home and away in March and need four points from those two games to secure passage to a playoff against the best team from the other Oceania group which contains Tahiti, Papua New Guinea and the Solomon Islands.
The winner of that tackles the South American side.
All Whites coach Anthony Hudson was satisfied with Tuesday's 0-0 draw with New Caledonia, even though they had their chances to win the game - Monty Patterson missed a gilt-edged chance - and the home side finished with only 10 men after captain Bertrand Kai was sent off for an ugly headbutt of Ryan Thomas.
New Caledonia also threatened at times and Bill Tuiloma was forced into a spectacular overhead kick to clear from the line midway through the second half.
"I am very vocal in saying that we want to win every game and at the beginning we set a goal of getting a minimum of four points from these windows," Hudson said.
"We would have liked to have done it [on Tuesday] obviously, but there were a lot of positives. It is a very difficult place to come."