The Euro 2016 champions took the lead on 33 minutes through a penalty from their captain, his 75th international goal, before Manchester City-bound midfielder Bernardo Silva knocked in a second from close-range only to pick up an ankle injury which saw him substituted at the break.
Forward Andre Silva wrapped up the comfortable victory with a fierce angled finish on 80 minutes and Nani added a fourth in stoppage time.
With hosts Russia losing against Mexico in Kazan, Portugal progressed as Group A winners, while the All Whites finished bottom following a third straight defeat.
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It remains to been seen who Fernando Santos' men will next meet in Kazan on Wednesday, but Real Madrid forward Ronaldo told reporters the focus now should be on lifting the trophy back at the Krestovsky Stadium on July 2.

Portugal's forward Cristiano Ronaldo (C) celebrates with teammates after scoring a penalty

Image credit: Getty Images

"We are very happy to be in the semi-finals," he said.
"We played very well, we wanted to win and get the result in the first half, (but) i t was hard to play better than we played because the grass (on the pitch) was not very good.
"We know that in the semi-finals both Chile and Germany are great teams, but we are confident and want to win."
While Chile and Germany are currently top of Group B, Australia or Cameroon could yet progress to the knockout stage with an unexpected victory on Sunday.
Portugal coach Santos said at a press conference: "I will analyse the opponents and prepare the game regardless of who we will play.

Cristiano Ronaldo (Portugal), buteur contre la Nouvelle-Zélande.

Image credit: Getty Images

"It is another phase, totally different, but the aim is to win.
"We have to be better and more consistent, stronger in both ways. You have to try to reach the goal and prevent them from scoring."
New Zealand coach Anthony Hudson felt his side could return home with plenty to build on despite not being able to register a victory.
"Overall, there were some really positive signs in the game," he said. "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.
"The biggest positive for me today was that we never, ever accepted the result. Every player went right to the end and there are so many positives I can take."
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