Taane Milne's successfully-converted penalty in the 62nd minute proved to be the difference, leaving the home fans stunned at the Wellington Regional Stadium.

Fiji's victory sets up a semi-final with Australia, who thrashed Samoa 46-0 in their quarter-final yesterday.

The match is scheduled to take place next Friday (November 24).

"We slayed a giant tonight," Fiji half-back Jarryd Hayne was reported as saying by BBC Sport.

"You don't see this very often but this win goes to our belief in God.

"We are in the business of slaying giants, it is the biggest test next week, it is as simple as that.

"We have a big week ahead of us and will prepare well."

An Apisai Koroisau penalty had given Fiji a 2-0 lead at the break before Shaun Johnson's boot restored parity within four minutes of the re-start.

But it was Milne who ultimately brought an end to a disappointing campaign for 2008 winners New Zealand, one of the tournament’s three host nations.

The Kiwis also suffered a surprise Group B defeat to Tonga as they ended up in the same half of the draw as holders and favourites Australia.

Earlier today, Tonga booked their place in the semi-finals after surviving a major scare to defeat Lebanon 24-22 at the Christchurch Stadium in New Zealand.

Lebanon were only six points behind at half-time and shortly after the break they had an Adam Doueihi try ruled out by the video referee.

Abbas Miski went over to reduce the deficit to two points with 10 minutes remaining, but the Middle Eastern nation were unable to register another score as Tonga held out to earn a spot in their first-ever World Cup semi-final.

David Fusitu'a scored two of Tonga’s four tries with Tuimoala Lolohea and Will Hopoate accounting for the others.

Miski’s late try was his second of the game, while Doueihi and James Elias also went over for Lebanon.

Tonga will next play either England or Papua New Guinea, who will contest the last of the quarter-finals at the Melbourne Rectangular Stadium tomorrow.