The South Americans asked soccer's world governing body FIFA to make the ruling, arguing that New Zealand had played fewer games in their qualifying rounds.
New Zealand featured in seven Oceania group qualifying matches plus a two-legged playoff, while Peru played 18 matches as they came fifth in their continent's competition.
"This resolution is an example that allows both national sides to start from an equal footing in the playoffs," FPF president Edwin Oviedo said on the federation's official website.
The teams meet in Wellington on Nov. 11, before heading to Lima for the second leg four days later to decide who goes to next year's finals in Russia.
(Reporting by Andrew Downie; Editing by Ken Ferris)
