If Portugal decide to record a song to accompany their passage to Brazil, maybe they will consider borrowing something from the Millwall pantheon in honour of their captain. No one likes him but he doesn't care, for Cristiano Ronaldo is going to the World Cup, and Zlatan Ibrahimovic is not.

On the day that the Portuguese newspaper Diário de Notícias reported that Ronaldo is set to open a museum in homage to himself next year on his home island of Madeira – with the help of his mother Dolores – Portugal's totem onceagain proved that there is brilliance beneath the bluster, delivering them to a major tournament via the play-offs for the third time in a row with a clinical hat-trick.

Ibrahimovic, the boy from the bad end of town who is now enough of a national treasure to merit a series of stamps bearing his image, scored twice and could have done little more to inspire Sweden. Yet the image of the night was the replay footage of Paris Saint-Germain's swashbuckling star simply applauding in the aftermath of Ronaldo's emphatically finished third goal, which killed the home side's challenge once and for all.

So was this his greatest performance for Portugal? "If you take it on the level of the goals then yes," Ronaldo said with a coy arch of the eyebrow, "but I've put in other great performances before, even without scoring. I made my contribution, at the very highest level. We deserved to win, and now it's about enjoying the moment."

He was right. There will be plenty of other times in the coming months for coach Paulo Bento to fret over Portugal's myriad flaws. "There's a lot to improve on," said Ronaldo but for now, friend and foe alike were compelled to join Ibrahimovic in admiration. It would be a surprise if the Ballon d'Or vote failed to follow suit.

His team-mate Miguel Veloso, like Ronaldo a Sporting Clube de Portugal product, summed it up succinctly. "The quantity of games he plays," he said, "the goals he scores, the situations he resolves … Ronaldo is a machine." Johan Elmander was similarly convinced. "[Ibrahimovic] did everything he could," said the Norwich striker, "but Ronaldo was just that little bit better."

He was so in a hostile environment too, as is the case so often on the road these days. The Friends Arena made it clear that it would not being living up to its name from the moment it loudly whistled Ronaldo's name as the starting lineups were read out to the crowd before the match, and the evening's events continued in a similar vein.

He quickly resumed hostilities with Mikael Lustig after their clash in Lisbon on Friday, with the Celtic defender snatching the ball impatiently from the Portugal captain's hands after the award of a free-kick in the opening seconds.

The main event, between Messrs Ibrahimovic and Ronaldo, was once again a slow burner in the first half. As is often the case for both, they seemed burdened with over-responsibility, trying to wrest the match to their individual wills single-handed.

"I knew that the national team needed me in these two games," Ronaldo said after the whistle to the Portuguese broadcaster RTP, and it shows.

While Sweden's talisman got sucked deeper and deeper to try to fill the creative void in midfield – just where Portugal wanted him – Ronaldo refused to look to pick passes. He wanted to grab the match by the throat.

Ronaldo's tendency to this first surfaced midway through the first period, when he thrashed a cross-shot over from a tough angle with others better placed for a pass. He vigorously berated his teammates for not taking up better positions, drawing catcalls from the stands and the evening's first chants of "Messi, Messi".

In among his 12 shots of the evening – three more than Sweden's team total of nine – the Real Madrid man almost created the opener for Hugo Almeida, but his recalled strike partner prevented a major incident from breaking loose by heading profligately into the side netting, with the hosts whistling for play to be stopped as Elmander lay injured.

What seemed as if it would be the definitive Ronaldo moment of the evening arrived in the 51st minute, as he sped on to João Moutinho's visionary through pass to move clear and strike left-footed past Isaksson. The Portugal bench certainly thought so, celebrating wildly, jumping and cavorting on the pitch.

Yet they needed him again after Ibrahimovic struck twice in four minutes, and this boisterous stadium caught the scent of blood. Portugal were panicking but their man reacted again, striking twice more in three minutes, in both cases from unforgiving angles. His last hat-trick, against Northern Ireland in Belfast, hauled Portugal out of a hole and took him past Eusébio's Portugal goal record. This one took him level with Pauleta, the national team's all-time leading scorer, on 47. It was another historic night for a historic player. His goal tally for the season is 32 from 22 matches, including five hat-tricks.

Confronted with the fact that Portugal will now have participated in as many tournaments in his decade-and-a-bit with the senior team – three World Cups and three European Championships – as in the whole of the rest of the country's footballing history, Ronaldo was surprisingly understated. "It's a coincidence," he said, for once giving himself less credit than the public at large. On current form, it could become a running theme.