Defending champions New Zealand hit top gear to demolish France and set up a semi-final against South Africa.
The All Blacks were almost out of sight at half-time, Julian Savea scoring two tries and Brodie Retallick and Nehe Milner-Skudder one apiece.
A try by Louis Picamoles had kept France afloat but when he was sent to the sin-bin French hopes evaporated.
Savea completed a fine hat-trick and Jerome Kaino, Kieran Read and Tawera Kerr-Barlow (two) also crossed.
France had hoped to draw inspiration from their World Cup upsets over the All Blacks in 1999 and 2007, when they beat them in the quarter-finals in Cardiff, as well as their near-miss in the 2011 final, when they narrowly lost 8-7.
But New Zealand, who have now beaten France nine times in a row and equalled Australia's record of 12 consecutive World Cup wins, never looked like losing against a Philippe Saint-Andre side forced to deny they are in outright rebellion.
And while the French simply did not have the requisite talent or a game-plan to trouble New Zealand, the performance of Steve Hansen's side was undoubtedly the most impressive of the tournament so far.
New Zealand started in breathless fashion and Dan Carter translated their pressure into three points after Thierry Dusautoir was penalised for not releasing.
France were level almost immediately, full-back Scott Spedding slotting a penalty from inside his own half, before second-row Retallick charged down a Freddie Michalak clearance kick and romped over for New Zealand's first try.
The All Blacks were nullified for a while by some stout French defence, until Ma'a Nonu and Conrad Smith, playing their 60th Test together in the centres, fed the ball to the brilliant Milner-Skudder, who conjured a try from nothing, stepping off his right foot and leaving the French defence for dead.
And when Julian Savea went over for New Zealand's 300th World Cup try, after a wonderful back-of-the-hand offload from Carter, France looked doomed.
Picamoles, France's inspirational number eight, had other ideas and latched onto a loose pass in front of New Zealand's posts and barged over, but when he was sin-binned for putting his fist in a prone Richie McCaw's face soon after the restart, the French challenge evaporated.
Savea had already grabbed his second just before half-time, the 6ft 4in, 17-stone wing displaying great strength to smash through three tackles and score his seventh try of the tournament.
And after Picamoles' departure Kaino trotted over unopposed before Savea finished from 40 metres out to equal Jonah Lomu and Bryan Habana's record of eight tries in an individual tournament and make it 38 tries in 39 Tests.
Some cute interplay between Charlie Faumuina and number eight Read ended with the latter touching down next to the posts, before replacement scrum-half Kerr-Barlow came off the bench to grab a clinical double as the world champions ran riot.
New Zealand rarely clicked despite topping Pool C, but four competitive matches appear to have been exactly what they needed in terms of sharpening them up for the knockout stages.
South Africa, who were shocked by Japan in their opening World Cup game, have mounted a stirring recovery and are battle-hardened after a bruising quarter-final victory over Wales.
But the All Blacks appear to have too much variety for the one-dimensional Springboks, who have beaten New Zealand only twice in their last 12 meetings.
Such a chastening defeat might be the best thing that could have happened to French rugby after the insipid reign of Saint-Andre.
When Toulouse coach Guy Noves takes over, the first thing he will have to address is his country's rugby philosophy, which is now less about flair and more about brute force, which on its own is rarely enough at the highest level.
However, Noves's biggest challenge will be attempting to persuade French clubs playing in the Top 14, who are often successful in European competition, to play in a more expansive manner. The post-mortem will be long and cruel.
What they said
New Zealand head coach Steve Hansen: "It was a very pleasing performance and everyone from number one to 23 played their part.
"We can't wait [to play South Africa]. We're playing against great opposition. They are a great team and we enjoy their company and we will enjoy playing them."
France head coach Philippe Saint-Andre: "Of course they [fans] are disappointed. I think we did the maximum, we tried and today New Zealand were much better than us.
"We worked hard for the last three months to be in this World Cup but each time we made a mistake New Zealand punished us.
"When the result is like this you have nothing to say and just congratulate New Zealand."