The All Whites creating several chances - with the best two falling to Chris Wood - but generally struggled to maintain possession - and Silva added a second in the 80th minute, before Nani's late strike.
Portugal are a class above Mexico and Russia, and picked a near full strength line up, including Cristiano Ronaldo, Andre Silva, Bernardo Silva and Pepe.
They seem to have a perfect blend; the touch and panache of a Latin American team, combined with the physicality and strength of European football.
It's hard to combat. The All Whites often managed to string together some promising movements, but were out dueled or wrestled off the ball.
Portugal opened the scoring through Ronaldo's penalty in the 33rd minute.
The European champions don't particularly need any help, but seemed to get a favourable call from American referee Mark Geiger.
Tommy Smith and Michael Boxall were guilty of blocking, but Danilo seemed to hook his foot under Smith's leg and went down very easily in the box. Given the magnitude of the occasion, it reminded a little of Daniele di Rossi's swan dive against the All Whites at the 2010 World Cup , though not nearly as blatant.
Ronaldo converted the spot kick, with unbelievable precision, and the goal let the pressure off, as frustration was just starting to build among the European champions.
They had dominated the flow of the game, and Ronaldo had hit the crossbar a few minutes earlier with a bullet header, but it wasn't all one way traffic.
The All Whites created the best early chance, with Dane Ingham finding Wood free in the box, but the Leeds striker dragged his shot straight at goal keeper Rui Patricio.
As they had done against Mexico, New Zealand was trying to play and managed to make some inroads into the Portuguese territory, with one diagonal pass from Thomas to Ingham comparable to anything seen at this tournament.
However, Portugal had always looked more likely, particularly with Ronaldo leaping like a salmon, and extended their lead in the 37th minute through Silva. The finish was simple, but the goal was made with a classy move down the left flank, catching out teenage wing back Dane Ingham.
The goal - which had come moments after coach Anthony Hudson had made an unusual first half substitution, switching Michael McGlinchey for Bill Tuiloma - could have deflated the New Zealanders.
Their body language wasn't great as they walked back to the centre circle - but this team showed they are made of sterner stuff. They held Portugal out - helped by two extraordinary reaction saves from Stefan Marinovic, with one off a Nani shot one of the best stops of the tournaments.
The All Whites also created some more chances, with the best falling to Wood at the far post after Tom Doyle found space and slid an inviting ball across the box.
But Portugal always looked more likely, and Silva grabbed his second in the 80th minute, a clean strike past Marinovic after running from halfway when Tom Doyle was caught dwelling on the ball.
The All Whites almost had the final say, with Michael Boxall's shot from four yards blocked on the Portuguese line, before Nani crunching 90th minute strike.
New Zealand 0
Portugal 4 (C Ronaldo 33 (pen), B Silva 37, 80, Nani 90)
Halftime: 2-0
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