Captain Mohamed Salah scored a goal and provided an assist as Egypt fought back from a goal down to record their first-ever win at the World Cup.
They are now top of Group H with four points after they were held to a 1-1 draw by Belgium in their opening game.
Iran are second with two points from as many matches, same as Belgium, while New Zealand are bottom on a point.
It was ninth time lucky for The Pharaohs after they did not win eight previous matches at the World Cup.
Egypt fell behind after just 15 minutes to New Zealand, before they turned it on with second-half goals by Mohamed Ziko, Salah and Trezeguet.
