- Goncalo Ramos (17', 51', 67')
- Pepe (33')
- Raphaël Guerreiro (55')
- Rafael Leão (90'+2')
- Manuel Akanji (58')
Head coach Fernando Santos made a brave call to drop Ronaldo following a dispute in their last match, but Portugal proved to be free-scoring without him, setting up a quarterfinal clash with Morocco on Saturday.
Ramos, making his first international start at age 21, opened the scoring at the Lusail stadium with a rocket strike inside goalkeeper Yann Sommer's near post before veteran defender Pepe, 39, became the oldest scorer in a World Cup knockout game with a thumping header.
Ramos struck again to start the second as he got on the end of defender Diogo Dalot's low cross and tapped home between Sommer's legs. Raphael Guerreiro made it four as he capped a well-worked team move with a powerful strike.
Switzerland struck one back on 58 minutes when Manuel Akanji found space at the back post from a corner and comfortably nodded in, but it did not spur a comeback, with Ramos striking his third with a deft chip over an onrushing Sommer, becoming the youngest male player to score a hat trick in a World Cup knockout match since Brazil legend Pele in 1958.
Ronaldo was brought off the bench on 72 minutes, and had a goal ruled out for offside, but Portugal still had time to net their sixth and final goal with a superb strike from substitute Rafael Leao in added time.
"Cristiano Ronaldo talks to me and everyone in the team. He's our leader and always tries to help," Ramos said after the match. "I don't know if I will start the next game, that's up to the coach, I have to work as hard as I can and then we'll see."
It was Portugal's first knockout victory since the 2006 World Cup in Germany, having suffered a group stage exit (Brazil 2014) and round of 16 elimination (South Africa 2010 and Russia 2018) since then.
After a tepid start, the game came to life when Ramos opened the scoring in the 17th minute by picking up Joao Felix's incisive pass before blasting the ball into the top corner from a tight angle to put the Portuguese ahead.
They doubled their lead through skipper Pepe when the 39-year-old timed his leap to perfection to rise above the two Swiss centre backs and head home from a Bruno Fernandes corner in the 33rd minute, with Sommer well beaten yet again.
At the other end, Switzerland striker Breel Embolo was frustrated by the Portugal defence despite the odd surging run into the final third, while their best chance of the half came when Xherdan Shaqiri's free kick was pushed out for a corner.
Sommer, returning from illness, did well to deny Ramos his second goal of the half with a fingertip save from a counter-attack as the Portuguese went in with a 2-0 lead at the break.
However, the beleaguered keeper could do nothing when Dalot sent in a cross six minutes after the restart with Ramos in the right place again at the near post to slip the ball between Sommer's legs and give Portugal a three-goal cushion.
"We did not show the mentality that we usually bring onto the pitch," Sommer said. "It is a very bitter evening. We gave the opponent far too much space. In a few situations I did not look too good either. This is not the way to survive against such opponents."
- César Arturo Ramos Palazuelos