The Real Madrid star struck from the penalty spot after 33 minutes. Bernardo Silva turned in a second goal for the European champions four minutes later.
Andre Silva added a third on 80 minutes before Nani completed the rout in stoppage time to ensure Portugal progressed to the last four as winners of Group A, finishing above Mexico on goal difference.
“We knew it could be complicated because we had seen New Zealand play Mexico and the problems they caused the Mexicans,” said Portugal coach Fernando Santos.
“I thought we played well in many parts of the game; in others, not so well. Overall though, it was a fair victory.”
New Zealand boss Anthony Hudson said the final result was harsh on his players. “We started the game really well and were the stronger of the two teams. But we had a period in that first half when we allowed them to come into the game and gave ourselves too much to do to get back into it.”
Mexico moved into the semis with a 2-1 win over Russia in Kazan. Aleksandr Samedov gave the hosts the lead after 25 minutes but within five minutes, it was all square. Hirving Lozano struck Mexico’s winner shortly after the pause and they will play the winners of Group A for a place in the final on 2 July.