The southern hemisphere's assault on the World Cup delivered the first two semi-finalists on Saturday when South Africa edged Wales 23-19 and New Zealand crushed France 62-13 to set up a titanic last-four clash between the rugby powerhouses.
Australia and Argentina will be looking to complete a Rugby Championship clean sweep by beating Scotland and Ireland respectively on Sunday.
Winger Julian Savea scored his second hat-trick of the tournament as the All Blacks steamrolled the French in Cardiff after a close game at Twickenham was settled by a moment of magic from Springboks scrumhalf Fourie du Preez.
New Zealand were far too strong for France, the side they overcame 8-7 in the 2011 final, sounding a clear warning that they do not intend to let go of their crown by winning the title abroad for the first time.
"We can't wait for the semi-finals, South Africa are a great team and we enjoy playing them," All Blacks coach Steve Hansen said after masterminding the biggest ever victory in a Rugby World Cup knockout match.
"New Zealand were two or three classes above (us)," said France captain Thierry Dusautoir.
Flyhalf Dan Carter kept his backs moving at pace and converted seven of the All Blacks' tries, adding a penalty for a personal tally of 17 points.
Lock Brodie Retallick, winger Nehe Milner-Skudder, flanker Jerome Kaino, number eight Kieran Read and replacement Tawera Kerr-Barlow (twice) also crossed the line.
The French replied with a first-half try from number eight Louis Picamoles, who was sin-binned in the second half.
The Twickenham quarter-final was defined by two Dan Biggar moments.
The Wales flyhalf, who kicked 14 points, laid on a fine try in the first half when he gathered his own perfectly judged kick ahead and as he was tackled passed to scrumhalf Gareth Davies who touched down under the posts.
Springboks flyhalf Handre Pollard kept his team's score ticking over with penalties and a drop goal and Wales, 13-12 ahead at halftime, went into the final six minutes clinging to a slender 19-18 lead.
DU PREEZ POUNCES
Biggar was then taken off as a precaution after receiving a knock to his head and in his absence a Welsh lapse of concentration at a Springboks scrum close to the touchline was exploited by Du Preez.
The Springboks forwards wheeled right and Duane Vermeulen dummied to go that way before turning and brilliantly offloading the ball to Du Preez who darted over in the corner.
Wales coach Warren Gatland had no complaints about the medical call on Biggar.
"He's done a fantastic job for us in terms of his leadership and control," Gatland said.
Unfortunately, that leadership of the back line was missing at the crucial moment and Du Preez seized the chance to apply a move the Springboks had rehearsed all week.
"We actually initially went for the penalty from the scrum, but during the week we noticed that their number nine was covering more behind the scrum and that opened some space," said Du Preez.
Argentina's Pumas, semi-finalists in 2007, face Ireland in Cardiff (1200 GMT) looking to prevent the Six Nations champions from reaching the last four for the first time.
The Irish have been further depleted by injury after flyhalf Johnny Sexton failed a fitness test on a groin injury on Saturday having been named in their starting line-up.
Ireland, who have replaced Sexton with Ian Madigan, had lost captain Paul O'Connell and blindside flanker Peter O'Mahony to injury. Openside Sean O'Brien is suspended.
Rugby Championship winners Australia, impressive in pool victories over England and Wales, should be too strong for Scotland at Twickenham (1500).
However, the Scots were boosted by news that forwards Ross Ford and Jonny Gray had won their appeals against three-week suspensions for foul play and are clear to face the Wallabies.