Rory Fallon, Michael McGlinchey, Moses Dyer and Rojas all scored from the spot for Anthony Hudson's side with Jeremy Brockie missing the fourth attempt.
Koriak Upaiga and Raymond Gunemka, however, also missed their two attempts to give New Zealand the victory and qualification for Russia next June.
The top six teams in the Nations Cup have advanced to the third and final round of World Cup qualifying next year, with the winner playing an inter-continental tie against the fifth-placed South American team for a spot in Russia 2018.
(Reporting by Greg Stutchbury in Auckland; Editing by Sudipto Ganguly)
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