New Zealand captain Daniel Vettori has called on his side to take their place in their first ever World Cup final after stunning South Africa in their last-eight encounter in Dhaka.

The Black Caps set the Proteas a modest target of just 222 for victory despite the best efforts of Jesse Ryder (83) and Ross Taylor (43), leaving Graeme Smith's men well placed to book a place in the semi-finals.

But the New Zealand attack had other ideas, with Jacob Oram and Nathan McCullum combining superbly to bowl the Proteas out for 172 and clinch a thrilling 49-run victory.

New Zealand now await the winners of Saturday's quarter-final clash between England and Sri Lanka, and skipper Vettori has backed his troops to maintain their momentum.

"We can beat any team on any day but consistency has avoided us a lot of the time," Vettori said. "It's our big chance. We're perennial semi-finalists at World Cups and hopefully we can take it one step further."

Vettori admitted his side's below-par efforts with the bat had forced their hand when it came to tackling the South African innings.

"With a score like 220 you know you've got to be aggressive and in a lot of ways the decision is taken out of your hands because you've got to keep attacking," he said.

"We managed to do that and pretty much every time I brought a bowler on they did the job and we got wickets."

South Africa's luck ran dry early on when Hashim Amla was out in the first over in bizarre fashion when his slice off Nathan McCullum bounced off wicketkeeper Brendon McCullum's foot to be caught by Vettori in the slips.

Smith and Jacques Kallis steadied the ship by putting on 61, but Oram hit back to dismiss the skipper for 28.

Kallis held firm on a turning wicket but a well-built 47 was ended by Tim Southee as Oram took a fine catch in the deep. Two wickets in the 28th over further dented South Africa's progress as JP Duminy was bowled by Nathan McCullum while AB de Villiers was run out after his patient 35.

And Vettori pointed to De Villiers' dismissal as the key moment in the game.

"The run-out of De Villiers was an amazing piece of work by Martin Guptil, and I could sense within the team that once we got that wicket, that's when we knew that we could win," he said.

Oram picked up the man-of-the-match award for figures of four for 39 and his superb running catch in the deep which removed Kallis.

"He's proved his worth in every game he's played," Vettori said of Oram.

"Four wickets and a great catch, you can't really ask for too much more."

Oram, meanwhile, admitted he was just enjoying being at the heart of the action after finally returning to full fitness after a string of injury setbacks.

"In the last couple of months my cricket's got better and that's just because I'm on the park," he said. "It's so hard when you're injured continuously to get some kind of rhythm and consistency going."

Asked whether the win would fuel belief in the camp that they can go on and win the competition, he said: "Why not? We've got to. We've just beaten a side who were the top qualifier from the other pool and are a damn good side. Why not take belief from it? If we didn't there'd be no point in playing.

"We've got a talented bunch of guys, unfortunately we're also inconsistent, but I've never been prouder to be in that dressing room and have the silver fern on."

For the defeated Proteas captain Smith, however, the feeling was one of abject misery after seeing his last six batsmen dismissed for just 51 runs.

"It's very difficult to explain how I feel, I've got no words to describe it," said Smith, whose career in one-day internationals was ended with this defeat.

"I've just got to take it on the chin. It's been a very disappointing evening. We've got to move forward in South African cricket now.

"I think we bowled reasonably well, and credit to Jesse Ryder, I thought he played really well. New Zealand kept a lot of pressure on us throughout our innings.

"We can only look at ourselves, we've let ourselves down, but I think all credit to New Zealand."