Heimir Hallgrimsson's team needed to win at the Puskas Arena to snatch a play-off spot in Group F ahead of its opponent, but Daniel Lukacs and Barnabas Varga struck either side of Parrott's 15th-minute penalty.

Ireland still trailed 2-1 with 10 minutes to play, before Parrott lifted a neat finish over Denes Dibusz to tee up a grandstand finish.

That was Parrott's second brace in as many games for his country, having scored both goals in Friday's memorable 2-0 upset of Portugal in Dublin.

The AZ striker became only the fourth player to score multiple goals in back-to-back matches, after Jimmy Dunne in 1936, Robbie Keane in 2013 and Callum Robinson in 2021, but the best was yet to come.

In the sixth minute of second-half stoppage time, the 23 year-old latched onto Liam Scales' flick-on and prodded home at the near post to spark wild Irish celebrations.

"I'm so emotional right now," Parrott said. "What a night, what a night.

"This is why we love football, because things like this can happen... I love where I'm from, my family are here, this means the world to me.

"I said against Portugal that this is what dreams are made of, but I think tonight... I will never have a better night in my whole life.

"It is a fairytale. You can't even dream about something like that. I have no words to describe the emotions right now."

Parrott's hat-trick is the first by any Republic of Ireland player on foreign soil, and it secured their place in the draw for the play-offs, which takes place on 20 November.

Parrott has 13 goals in 14 games at club level this term – six in the Eredivisie and seven in Conference League qualifying – and Hallgrimsson believes he would be among Europe's most prolific players if not for a knee injury that plagued him in the season's early weeks.

"He should enjoy this moment," the Ireland boss said. "Sadly for him, he got injured for a long spell early in the season, or he would have been one of the top scorers, if not the top scorer, in Europe.

"He's just shown his quality. But this moment shouldn't be about finding heroes; it should be this team, the spirit, unity and hard work this team showed."

Portugal topped Group F, finishing three points clear of Ireland after a 9-1 rout of Armenia in its final game, while Hungary was eliminated after finishing third.