Cristiano Ronaldo, Bernando Silva, Andre Silva and Nani all got on the scoresheet as the Euro 2016 winners finished top of Group A ahead of Mexico, who claimed the runners-up spot after registering a 2-1 triumph over hosts Russia.
Portugal went into the match knowing that victory would be enough to secure their place in the last four of the competition, while New Zealand were playing for pride after losing to both Mexico and Russia.
Slowly but surely, Portugal began to gain control of the contest but it took until the 24th minute for Ronaldo to force a stop out of Stefan Marinovic with a header at the near post.
With 12 minutes of the half remaining, however, Ronaldo gave Portugal the lead from the penalty spot after a foul by New Zealand's Thomas Doyle gave him the chance to net from 12 yards.
It did not take long for the European champions to double their advantage through Bernando Silva, who confidently found the back of the net after receiving a pass inside the penalty box.
During the early stages of the second half, Portugal were dealt a blow when Pepe picked up a booking which will sideline him for the semi-finals, and they were given a reminder that New Zealand were still active in the game when Wood saw a goalbound effort cleared off the line.
However, as the encounter entered the final quarter, Portugal upped the tempo and Nani should have scored from close range, only to see Marinovic pull off a stunning save to divert the ball for a corner.
Up the other end, Wood tested Patricio with a long-range drive but 10 minutes from time, Andre Silva scored Portugal's third after he ended a lengthy run with a shot into the top corner of the net.
It appeared that the scoring in St. Petersburg had ended but in the first minute of added-on time, Nani found the bottom corner of the net from 16 yards to wrap up a convincing success.