Hosts New Zealand and twice champions Australia set up their third World Cup semi-final on Sunday after the All Blacks defeated Argentina 33-10 and Australia scraped an 11-9 win over defending champions South Africa.
Battle will resume at Auckland's Eden Park next weekend where Wales will play France on Saturday followed by the All Blacks versus the Wallabies a day later.
A final on October 23 between the remaining two teams from each hemisphere was guaranteed once Ireland upset twice champions Australia in the pool stages to ensure a quarter-final against Wales.
New Zealand, seeking their first World Cup since the inaugural 1987 tournament, lost to the Wallabies in the 1991 and 2003 semi-finals.
They will, though, be boosted by the knowledge that no side has won the Webb Ellis trophy after losing in the group stages.
"Positive sides did well (in the quarter-finals) and that's fantastic for the game," Australia coach Robbie Deans said.
"In the next couple of weeks, I have no doubt will be some of the best World Cup rugby we've ever seen because the bar just keeps going up in terms of the capability of all the sides."
Argentina, who finished third at the 2007 tournament after defeating hosts France in the opening match and the third place playoff, belied their first round form with a splendidly defiant performance against the All Blacks at Eden Park.
They even took the lead briefly in the first half with the first try of the match, scored against the run of play by flanker Julio Fariaa Cabello. However, New Zealand kept their shape and late tries to forwards Kieran Read and Brad Thorn put the issue beyond doubt.
In the absence of the injured Daniel Carter, man-of-the-match Piri Weepu calmed the fears of a nation willing their heroes to victory with seven penalties.
New Zealand were also relieved by the display of Aaron Cruden, their third choice flyhalf behind Carter and Colin Slade, who left the field injured in the first half.
Cruden grew in stature as the match progressed and Weepu's prowess with the boot settled any debate about the first All Blacks' halfback combination for the remainder of the tournament.
The third of the weekend's quarter-finals, after Wales beat Ireland and France upset England on Saturday, played on a still, sunny day at the Wellington Regional Stadium, proved no advertisement for southern hemisphere rugby.
Both teams produced a series of basic handling and kicking errors which had the crowd groaning in disbelief.
The match statistics proved an indictment of the Springboks' sterility on attack. They won 76 percent of the territory, 56 of the possession and stole five Australian lineouts and one scrum.
Despite this overwhelming advantage they could not score a single try, although fullback Pat Lambie crossed the Australia in the second half but was called back for a forward pass.
In the end, the most significant statistic was the 147 tackles the Australians were forced to make to repel the most experienced South African side ever to take the field.
"We had some real issues clearing the ball in the second half and they put us under a lot of pressure but I'm really, really proud of the way the guys fought," said Australia captain James Horwill, who scored the only try of the match.
"We knew that defence wins these big games and our discipline was really good."