Although Egypt already looked like the stronger team and had more possession, the opening goal came from New Zealand through a header from Finn Surman in the 15th minute.
In the second half, however, Egypt took control of the game. World Cup debutant Mostafa Ziko was the first to equalize, and just minutes later he set up star player Mohamed Salah to take the lead.
Egypt's David Trezeguet then added a third after just a few minutes on the pitch.
New Zealand, the lowest-ranked of all World Cup teams, will face Belgium in their next match while Egypt plays Iran.
