Andre Silva wrapped up a comfortable victory with a fierce angled finish on 80 minutes, and Nani added a fourth in stoppage time.
The progress means Portugal are on course for a second trophy in two years, but will have to first pass their semi-final test on Wednesday.
Coach Fernando Santos is not concerned about which team is up next for Portugal, with Group B to be decided on Sunday. "We're confident and want to win", said Ronaldo, who picked up his third straight man-of-the-match award in Russian Federation.
"Overall, there were some really positive signs in the game", he said.
"We knew it could be complicated because we had seen New Zealand play Mexico and the problems they caused the Mexicans. We never stopped. We created chances, we put them under pressure, so we could have got a little more out of this tournament", he told reporters.
Despite having a man less though the hosts showed real spirit to try and get an equaliser and they should have got it when Igor Smolnikov, who had just came on as a second half substitute, missed from a few yards out after a fantastic cross found unmarked in the box.
Needing a victory to advance from their hard group, Russian Federation played well and took the lead with a goal by Alexander Samedov in the first half, but the experienced Mexico side equalised with Néstor Araujo before half-time and secured the win early in the second half with a goal by Hirving Lozano after a blunder by the goalkeeper Igor Akinfeev.
Following a strong showing in a 2-1 defeat to Mexico three days earlier, the clash with the world No 8 Portuguese was always going to be a stiff task for 95th-ranked New Zealand.More news: Senate health care bill adds 22 million uninsured, says Congressional Budget Office
Captain Cristiano Ronaldo put Portugal ahead from the penalty spot on 33 minutes.
Four minutes later, Bernardo Silva slipped a shot into an unguarded goal.
Marinovic made impressive saves to deny Ronaldo, Andre Silva and Nani but was powerless stop Andre Silva when he collected the ball on the halfway line, ran at two defenders who backed off, and fired his shot into the far corner.
He joins Cristiano Ronaldo in that club and, naturally, the tournament superstar brought up yet another milestone with his 75th worldwide goal.
Akinfeev made a mistake that led to Mexico's second goal after a long clearance by Herrera from near the south American side's area. New PSV Eindhoven signing Lozano then headed Mexico into the last four as he beat Russian Federation goalkeeper Igor Akinfeev to Hector Herrera's towering kick from inside his own half on 52 minutes.
Cristiano Ronaldo's 75th global goal helped lift Portugal to the semifinals.
Hosts Russia took a deserved 25th-minute lead in Kazan through Aleksandr Samedov, but Nestor Araujo equalised for Mexico with a looping header on the half hour.
Other teams in Group A includes Mexico and the host, Russia.